Category: Timeline Stories

The British statesman and versatile scientist Charles Stanhope, Viscount Mahon, was a very strange peer—a full of temperament man with enormous mental energies, voice, and earnestness, who devoted a large part of his time and income not to pleasures and parties, but to experiments, science, and philosophy.

Interestingly, in the 1770s the young Stanhope spared a significant part of his time to the developing of calculating machines, devising a total of three calculating devices, as well as a logic machine (so-called Demonstrator). All the calculating machines (so-called arithmetical machines) of Stanhope were manufactured by the skilled clock-maker James Bullock (they are inscribed on the cover: ”Visc(oun)^t Mahon Inv(enit) 1780 Ja(me)^s Bullock Fecit“ – invented by Viscount Mahon, made by James Bullock), the first machine—in 1775, second—in 1777, and the last—in 1780.

First thought of building a calculating machine appeared to the young Charles Stanhope probably at the beginning of the 1770s, when he studied at the University of Geneva. There his teacher in mathematics was Georges-Louis Le Sage, an inventive man with whom he conducted extensive correspondence. Through him, Stanhope might have heard of earlier attempts to develop such a device, as Pascaline of Pascal and Stepped Reckoner of Leibniz.

The calculating machines of Stanhope typify his obsession with technical innovation whilst retaining a practical, rather than theoretical application. Indeed, he never sought financial reward for any of his inventions—which over time badly drained his fortune—preferring to see them, like his politics, as the practical means to a more enlightened age.

The first calculating machine of Stanhope

In his first calculating machine (made in 1775) Stanhope used the well-known stepped drum of Leibniz, which teeth however are not smooth, but are presented in the form of teeth-strips (strips with 1 to 9 teeth). This type of mechanism will be later used in other machines and will be called an adapted stepped drum or adapting segment.

The machine is closed in a fine mahogany case with overall dimensions: 9 x 45 x 17.5 cm, and a weight of 9 kg.

The calculating mechanism contains twelve adapted stepped drums (see the photo below), mounted on axes in a special movable carriage. To the axes are attached digital wheels (dials), and to each digit of the dial corresponds a strip of the drum with the appropriate number of teeth (i.e. to digit 0 corresponds the smooth surface of the drum, to 1—a strip with one tooth, etc.).

During the calculations, the carriage is moved, and during this movement teeth-strips will be engaged with the gear-wheels of the main counter and will rotate them according to the teeth of the strip. This action first transfers the entered number into the result mechanism and then performs the tens-carry steps, if needed. There is also a secondary counter, which counters the number of the moving of the carry and is used during multiplication/division. The machine also features a place-shift mechanism to allow multi-digit multipliers and to facilitate division.

During multiplication, the multiplier is set at the beginning and when zero is reached, the multiplication is complete. This course of action also facilitates subtraction and division, as the counter rises from zero to the answer. To prepare the machine for this type of work, a toggle lever at the side is moved until a D appears in the window to the right instead of an M. This action reverses the process during the push-and-pull of the carriage: the transfer to the result mechanism now takes place in the second step, with all rotations reversed, and the tens-carry steps are performed in the first step. However, this method of work has the disadvantage that the tens-carry steps arising in the second step are not carried out. Stanhope solved the problem by incorporating an additional small white-handled crank at the left side with which any outstanding tens-carry steps can be done.

The tens carry mechanism of the machine is rather complex and innovative. In fact, Stanhope is the first inventor (although in the sautoir of Pascaline there is something similar), who separated the tens carry operation into two phases: a preparation phase, which is done when the digital wheel rotates from 9 to 0, and the execution phase, which is done during the movement of the carriage. Some 100 years later this 2-phase operation of tens carry will be widely accepted by the mechanics, because this mode of operation removes the very nasty effect of accumulation of strength in the mechanism.

The second calculating machine of Stanhope

The internal mechanism of the machine from 1777 (see the photo below) is similar to the first machine, as it used again Stanhope’s adapted stepped drum mechanism. However, in the second machine the linear movement, used in the first machine, is replaced by the more convenient and fast rotating movement, so it is more suitable for multiplication and division. The tens-carry mechanism was improved as well.

The second machine of Stanhope is also closed in a fine mahogany case and was made of brass, iron, and ivory (handles). Its overall dimensions are: 36 x 22 x 21 cm, its weight is: 9 kg.

Multiplication and division are performed by repeated addition and subtraction with intermediate carriage movements, using a 12-place revolution counter operated by a lever connected to the setting mechanism.

This machine is the first in which tens-carry operation was fully automatic. Whenever one of the figure-wheels at the back is moved from 9 to 0 in addition (or from 0 to 9 in subtraction), a pin projecting from it trips a corresponding spring-loaded tumbler. Below the figure-wheels and tumblers is a shaft. As the cycle continues, teeth on the cam wheel engage a gear on this shaft so that it makes one full revolution; arms on the shaft sweep round and reset any tumblers that have been tripped, and in doing so move the next figure-wheel to the left by one place. The arms on the shaft are set in a helical pattern, so that these carrying operations take place one after another from right to left, allowing for the possibility that one carrying will lead to another in the next place up. Two sets of arms are fitted, spiraling in opposite directions, and two sets of teeth on the cam wheel make the shaft rotate at two different times during the rotation of the drum. These duplications ensure that the carrying operation is fully performed, whether the machine is rotating forward for multiplication or backward for division.

Stanhope’s first calculating machine (from 1775) was an innovative device, which has however several flaws, but by creating his thorough second machine in 1777, he demonstrated that he was able to build an elaborate and fully functional 4-species device. Thus he counts as one of the most innovative inventors of mechanical calculators of the 18th century.

The prototypes of the first two calculating machines of Stanhope were eventually acquired by Charles Babbage, passed down to his son Henry P. Babbage, and given by him to the Victoria and Albert Museum in London in 1905. Besides these two machines, kept now in Science Museum, London, another device survived to our time and is kept at the Stanhope’s mansion in Chevening, Kent.

Despite using the stepped drum of Leibniz, Stanhope’s first and second machines are quite different from earlier machines in nearly every respect and seem an original invention.

The third calculating machine of Stanhope

Interestingly, the last calculating machine of Stanhope (from 1780) is the simplest of his three devices, being a small and simple adder. The only surviving to our time example is kept now in the collection Museum of the History of Science, Oxford. The device resembles the earlier adding machine of Samuel Morland.

The third calculating machine of Stanhope was a small and simple adding device with dimensions: 2.2 x 23.2 x 7.5 cm, and a weight of about 900 g.

Stanhope’s adding device has 12 digital positions (dials). The first eight (leftmost) dials are decimal and are labeled HM for hundred million, XM for ten million, M for millions, HT for hundred thousand, XT for ten thousand, T for thousands, H for hundreds, and X for tens. The next four dials are labeled L for pounds, S for shillings, D for pence, and F for farthings. This is the old English system of money, used until 1971 (4 farthings = 1 penny, 12 pennies = 1 shilling, 20 shillings = 1 pound sterling).

The rotating of the dials and entering of the numbers is done by means of a stylus, which can be put in the openings in the periphery of the dials. The dials are successively connected within the mechanism by means of wheels with just one cog, thus the tens carry mechanism was difficult to use, having a problem with the transfer of forces.

The Demonstrator of Charles Stanhope

Charles Stanhope worked on his logic machines for some 30 years, creating several versions. On the lower image is shown a circular version of his Demonstrator, created in the late 18th century.

The most effective version of the device was the rectangular one (see the lower image), created at the beginning of the 19th century.

Stanhope’s Demonstrator was designed as a device able to solve mechanically traditional syllogisms, numerical syllogisms, and elementary probability problems. The rectangular version of the device consists of a brass plate (size 10 x 12 x 2 cm), affixed to a thin mahogany block. On the brass face, along three sides of the window, integer calibrations from zero to ten were marked. In the center, there is a depression (4 cm in area and 2.5 cm deep), called the holon. Across the holon two slides can be pushed; one, set in a slender mahogany frame, is of red transparent glass and works through an aperture on the right. The other is of wood and is called the gray slider. In working the “Rule for the Logic of Certainty” this slide is passed through an aperture to the left; but in working the “Rule for the Logic of Probability”, it is drawn out and inserted in an aperture at the top, when it works at right angles to the red slide.

To solve a numerical syllogism, for example:

Eight of ten A’s are B’s;
Four of ten A’s are C’s;
Therefore, at least two B’s are C’s.

Stanhope would push the red slide (representing B) eight units across the window (representing A) and the gray slide (representing C) four units from the opposite direction. The two units that the slides overlapped represented the minimum number of B’s that were also C’s.

To solve a probability problem like:

Prob (A) = 1/2;
Prob (B) = 1/5;
Therefore, Prob (A and B) = 1/10.

Stanhope would push the red slide (representing A) from the north side five units (representing five-tenths) and the gray slide from the east two units (representing two-tenths). The portion of the window (5/10 x 2/10 = 1/10) over which the two slides overlapped represents the probability of A and B.

In a similar way, the Demonstrator could be used to solve a traditional syllogism like:

No M is A.
All B is M.

Therefore, No B is A.

The Demonstrator had obvious limitations. It could not be extended to syllogisms involving more than two premises or to probability problems with more than two events (always assumed to be independent of one another). Any of the problems it could handle were solved easily and quickly without the aid of the machine. Actually, Stanhope designed his devices for demonstration purposes, as can be seen by the name Demonstrator, not for solving real-life problems. He wrote “As the instrument is so constructed as to assist us in making demonstrations, I have termed it Demonstrator. It is so peculiarly contrived as likewise to exhibit symbolically those proportions or degrees of probability which it is the object of the Logic of Probability to discover”.

Stanhope bases his system on what De Morgan will call later the arithmetical view of the proposition; and this view determines the form of his method of mediate inference and leads to an extension of the common doctrine. He proposed a rule “for discovering consequences in logic”, which is a remarkable anticipation of that given by De Morgan from the numerically definite syllogism.

Nonetheless, Stanhope believed he had made a fundamental invention. The few friends and relatives who received his privately distributed account of the Demonstrator, The Science of Reasoning Clearly Explained Upon New Principles, were advised to remain silent lest “some bastard imitation” precede his intended publication on the subject. This publication never appeared and the Demonstrator remained unknown until the Reverend Robert Harley described it in an article in the journal Philosophical Transactions in April 1879. Let’s see the article: “The Stanhope Demonstrator: An Instrument for Performing Logical Operations”:
Earl Stanhope’s Demonstrator is much less powerful as a logical instrument than Professor Jevons’ machine, but the former is undoubtedly a distinct anticipation of the latter. It is probably the first attempt ever made to solve logical problems by mechanical methods. Both in his quantification of the predicate and in his solution of problems involving numerically definite propositions, we see the Earl struggling, not unsuccessfully, to escape into some less confined system of logic than that of Aristotle. He shewed little respect for the authority of the ancient logicians. The same reforming zeal which he displayed in politics he exhibited also in the treatment of logic. He brought to the study of the subject a certain independence and originality of thought which led him to examine the foundations of the science for himself. “I intend,” he declared, “to exclude entirely that long catalogue of pedantic words which are now used for the purpose of drawing consequences, and which are, generally speaking, both unintelligible to youth and unfit for men of any age, so far at least as relates to convenient and habitual use. My system of logic will, on the contrary, be found to have the striking advantage of uniting simplicity, perspicuity, utility, and perfect correctness. The science requires to be totally reformed.”
The materials do not enable us to give a complete or systematic account of Stanhope’s views on logic. Even on the working of his Demonstrator we find in his remains no full or formal statement, but only scattered and fragmentary limits, and a very few simple examples. It is possible, therefore, that in the hands of its noble inventor the instrument possessed a range and power somewhat greater than is apparent to us. He attached to it a practical importance; for us it possesses little more than a theoretic or historic interest. “It exhibits the consequences symbolically,” he wrote, “and renders them evident to the mind. With the aid of this instrument the accuracy or inaccuracy of a conclusion is always shewn, and the reason why such consequences must of necessity exist is rendered apparent. As the instrument is so constructed as to assist us in making demonstrations, I have termed it the Demonstrator. It is so peculiarly contrived as likewise to exhibit symbolically those proportions or degrees of probability which it is the object of the Logic of Probability to discover.”
All propositions are reduced by Stanhope to one form, namely, the expression of the identity of two or more things or classes of things. This “method of identification,” as he calls it, is illustrated by numerous examples. For instance, “Hardness belongs to diamonds,” means that ” Some of those things which possess the quality of hardness and all diamonds are identic.” “Some printing presses cannot be worked without great labour,” means that “Some printing-presses are identic with some of those instruments which cannot be worked without great labour.” In these examples, we recognize an anticipation of Mr. George Bentham’s four forms of affirmative propositions, forms which were afterwards adopted by Sir William Hamilton.
Stanhope bases his system on what De Morgan calls the arithmetical view of the proposition; and this view determines the form of his method of mediate inference and leads to an extension of the common doctrine. He proposes a rule “for discovering consequences in logic,” which is a remarkable anticipation of that given by De Morgan from the numerically definite syllogism. It is a noteworthy fact that he does not limit the rule to a special form but puts it forth as embodying the fundamental principle of all syllogistic ratiocination.
The Demonstrator consists of a brass plate 4.5 inches long and 4 inches wide, affixed to a thin block of mahogany. In the centre there is a depression 1.5 inches in area and half an inch deep, called the holon. Across the holon two slides can be pushed; one, set in a slender mahogany frame, is of red transparent glass and works through an aperture on the right. The other is of wood, and is called the gray slider. In working the “Rule for the Logic of Certainty” this slide is passed through an aperture to the left; but in working the “Rule for the Logic of Probability,” it is drawn out and inserted in an aperture at the top, when it works at right angles to the red slide. Stanhope devised several other instruments of various sizes and construction; but they are both less simple and less effective. It does not seem possible for the Demonstrator in its present form to solve very complicated questions. It is constructed for problems involving only three logical terms; but additional slides would increase its range and power. To Stanhope belongs the honour, and it is a very high honour, of being the first (probably) to attempt the solution of logical problems by a mechanical method. There may be some difference of opinion as to how far he succeeded, but there can be none as to the ingenuity of the attempt. The contrivances of earlier logicians, especially the circles of Euler, probably prepared the way; but Stanhope did undoubtedly take a very important step in advance when he constructed his Demonstrator. His conversion of all propositions into the form of identities by means of the quantification of the predicate, and the principle of his mechanical method, namely, that the process of mind involved in the ordinary syllogism and that involved in the numerically definite syllogism are essentially the same, must be regarded as distinct contributions to logical science and as remarkable anticipations of recent discoveries.

The Demonstrator was important mainly because it demonstrated to others, most notably to William Jevons, that problems of logic could be solved by mechanical means.

Biography of Charles Stanhope

The British politician and man of science Charles Stanhope, 3rd Earl Stanhope and Viscount Mahon, was born in London on 3 August 1753, as the second son in the noble and rich family of Lord Philip Stanhope (1714-1786), 2nd Earl of Stanhope, a British peer, Fellow of the Royal Society and a conspicuous figure in the scientific world, and Lady Grizel Hamilton Stanhope (1719-1811). Philip Stanhope (see the lower portrait) married Grizel Hamilton, daughter of Charles Hamilton, Lord Binning, on 25 July 1745 and they had two children: Philip (1746-1763), and Charles.

Charles was sent very young (only nine years old) to Eton College in Windsor, where studied his brother Philip. Unfortunately, Philip, a very talented boy, inherited from his mother’s family the tendency to consumption, which had proved fatal to so many of the Hamiltons. He was removed to the purer air of Geneva, Switzerland, together with his mother, but eventually, he died on 6 July 1763.

Charles now became Viscount Mahon and the heir to the peerage, and, as the only surviving child, was more than ever the object of his parents’ solicitude. They resolved that his health should not be exposed to the English climate, or the care of his mind to the capricious attentions of the English schoolmaster. He was recalled from Eton, and the family decided on settling in Geneva in July 1764.

The family continued in Switzerland for ten years, where young Charles had been educated at Leyden and Geneva under the inspection of the prominent Swiss scientist Georges-Louis Le Sage (1724-1803). He learned Greek and French and applied himself eagerly to mechanics, philosophy, and the higher branches of geometry, but not to the classics and fine arts. At seventeen, Charles won the prize offered by the Swedish Academy for the best essay on the construction of the pendulum.

At the age of 20, still in Geneva, Stanhope was already proven as a promising scientist and good athlete (he rode well, played bowls and cricket, and acquired some skills in shooting and skating). In February 1774, Stanhopes set out from Geneva, with great marks of friendship and honour shewn then on leaving notre seconde patrie. They stayed several months in Paris, and in July 1774 they returned to England.

In September of the same 1774, Stanhope proposed to Lady Hester Pitt (1755-1780, see the nearby portrait), his second cousin and a sister to his friend William Pitt the Younger, the future English prime-minister, and was accepted. The couple married on 19 December 1774, at St. Mary the Virgin church in Hayes. Two years later was born their first child—a daughter, who will become the famous British socialite, adventurer, and traveler Lady Hester Stanhope (12 March 1776 – 23 June 1839). Stanhope had two other daughters from this marriage (Griselda, born 1778, and Lucy Rachel, born 1780), before the early death of Lady Hester (Pitt) Stanhope, on 18 July 1780, of complications following the birth of their third daughter.

The death of Stanhope’s first wife was a tragedy for him, for neither his second wife nor his children inspired him with deep affection.

In January 1775, Stanhope was admitted to the Royal Society, to which he had been elected in 1773 before leaving Geneva. Stanhope’s chief interest outside politics was applied science, and he was acquainted with most of the scientific men of his day. The great drawing room at his Chevening estate was turned into a laboratory.

In 1880 Stanhope became a member of the House of Commons, upon the death of his father in 1786, when he took his place as a Peer of the realm on 7 March 1786.

Lord Stanhope was a very strange peer—a man with enormous mental energies and earnestness, who devoted a large part of his time and income not to pleasures and parties, but to experiments, science, and philosophy. According to the memories of his contemporaries, he was a tall and thin man (he was frequently compared to Don Quixote, whom he resembled not only in appearance, but still more in valour and high-mindedness), who looked pale, but had a very powerful mind and voice and used to wave his arms around a lot when he was explaining things.

In 1781 Charles Stanhope married his deceased wife’s cousin-german, Louisa Grenville (1758–1829), the daughter and sole heiress of the British diplomat and politician Henry Grenville. Louisa was the mother of three surviving sons, the first of them—Philip Henry Stanhope (1781–1855) inherited not only the title Earl Stanhope, but also many of the scientific tastes of his famous father. It was an unhappy marriage, and in the coming years Charles, 3rd Earl Stanhope after 1784, would fall out with all six of his children, become estranged from his second wife, and take up with a music instructor.

Lord Stanhope was most known by his contemporaries as a politician, but his reputation with posterity depends more upon his talent as a philosopher, scientist, and inventor. Politically he was revolutionary, opposed the slave trade, as well as the war against France, which earned him the nickname Citizen Stanhope, and was a supporter of education and electoral and fiscal reforms. His lean and awkward figure was extensively caricatured by his contemporaries.

Stanhope was an active member of the Royal Society. He wrote a very interesting treatise on electricity. The Lord devoted much attention to the means of preserving buildings from fire. Another object, which took a considerable share of Stanhope’s attention was the employment of steam for the propulsion of vessels, for such experiments he expended very large sums. He shared his knowledge with the inventor of the first commercially successful steamboat—Robert Fulton (1765-1815).

Stanhope’s most significant contribution was to the printing industry. He is well known for suggestions for improvement in the construction of the printing press and as an early patron of the stereotype method of printing. He created a printing press with original construction (see the photo below), which will become very popular all over the world in the next century.

Alongside the ‘Stanhope Press’—a sophisticated iron hand-press with a novel lever and screw mechanism which was used to print The Times until the arrival of steam presses, Stanhope developed a system of logotypes and perfected a means of stereotyping adopted by both Oxford and Cambridge University Presses. Characteristically, Stanhope was driven in these projects by a desire to propagate learning through cheaper schoolbooks though they, yet again, placed a severe burden on his own finances. They also exacted a heavy price on his private life.

Stanhope invented also optical lens, which bear his name, and a method for tuning musical instruments.

Chevening House is a large country house in the parish of Chevening in Kent, in southeast England. The house was the home of the Stanhope family for almost 250 years before it was placed in trust for the nation on the death of the 7th Earl in 1959.

Stanhope’s life was thus one of unremitting toil. He died of dropsy in his family seat in Chevening, Kent, on 17 December 1816, and was buried at Stanhope Chantry in St. Botolph Churchyard, Chevening. Friend and foe agreed that in the third Earl Stanhope one of the most striking personalities of his time had passed away. Throughout his life, Stanhope deservedly enjoyed a great reputation for his discoveries in science, and Lalande called him the best English mathematician of his day.

Jacob Auch (1765-1842) was a very good German mechanic and clock-maker, who created about 1790 a calculating machine not of original construction, but of very good workmanship.

Auch was born in Echterdingen, a small town in the district of Esslingen, in Baden-Württemberg. In the same town, from 1781 till 1790 served the famous German pastor and engineer Philipp Matthäus Hahn.

The young Jacob worked six years in Hahn’s workshop in Echterdingen and proved to be his best apprentice. At some moment Auch decided to start his own business, and in 1787 he opened and worked in his workshop in Vaihingen an der Enz and Karlsruhe, where he stayed until 1798, when he was hired as a Ducal Mechanic (Großherzoglichen Hofmechanicus) at the Weimar court, where he stayed until his retirement in 1842.

During the years 1789 and 1790, while in Vaihingen an der Enz, Jacob Auch made several adding machines of very good workmanship. He was obviously inspired by the adding machine of his mentor Hahn, as its construction is quite similar to the adder of Hahn, but has an improved tens-carry mechanism.

It is unknown how many machines have been produced by Auch, but at least three survived to our time—one in Württembergisches Landesmuseum in Stuttgart, dedicated to the Margrave Karl Friedrich von Baden (signed: Jacob Auch Vayhingen, see the lower images), second in Matematisch-Physikalischen Salon in Dresden, and third in Boerhaave museum (Rijksmuseum Boerhaave), Leiden, Netherlands (see the upper image).

The dimensions of the machine of Auch in Stuttgart are: 22,8 x 6,1 x 1,9 cm (the device in Leiden is bigger—28 x 8,0 x 4,0 cm), and the weight is about 720 g. It is made mainly of brass and is placed in a wooden case.

The “Stuttgart machine” of Auch has eight digital wheels, as seven of them are decimal, and one (the second from the right) is divided into 12 parts (the Leiden device is destined for another monetary system and has a 24 parts wheel). The graduation of the disks was made according to the monetary system adopted throughout the southern states of the Holy Roman Empire in the 18th century (60 Kreuzer = 1 Gulden). The two rightmost wheels are used for calculations in Kreuzer (12 x 10), and others (decimal) are used for Gulden. Entering the numbers can be done by means of a stylus.

At the lower left corner of the box is inscribed a short instruction for work in German: use black to add and red to subtract. This means, that the internal calculating mechanism is unidirectional, the wheels can be rotated only in the clockwise direction, and subtraction can be done, using the method complements of 10.

The calculating machine of Auch has an improved tens-carry mechanism. This important constructional element of the machine used the so-called tens-carry-rail, which guarantees reliable tens-carry operations. The machine also has a memory mechanism for storing numbers.

Biography of Jacob Auch

Jacob Auch was born on 22 February 1765, in Echterdingen (near Stuttgart, Württemberg), to Johann Andreas Auch (1733–1787), a baker, and Christina Henn (1736–1782). Jacob had a younger brother, Johann Georg (2 Jul 1766-24 Aug 1838), who also became a clock-maker and mechanic.

When Jacob turned sixteen, his father wanted to put his elder son into a trade, and initially planned for him to become a barber, but Jacob had absolutely no taste for this vocation. Fortunately, in his hometown, Echterdingen, in 1781 was appointed a new pastor – the famous German engineer Philipp Matthäus Hahn. Thus the young Jacob became an apprentice of Hahn and used to work for six years in his workshop in Echterdingen. Hahn was a severe taskmaster, but Jacob Auch soon proved himself as the most talented and ambitious apprentice of Hahn, so in 1887 he decided to go in his own way, establishing a family and his own workshop, and he was very successful in his career as a watch-maker and mechanic.

On 11 July 1787, in Vaihingen an der Enz, Auch married to 22 years old Eva Regina Wintermantel, a daughter of Johann Christoph Wintermantel (1738–87) and Anna Maria Wintermantel (née Roselius), and in the same year, he opened his own workshop in Vaihingen. They had one (survived adulthood) child – the son Johann Jacob Auch (1789-1885). Auch stayed for more than 10 years in Vaihingen, and during this period he fulfilled many orders of the professor of mathematics and physics from the Institute of Physics in Karlsruhe Johann Lorenz Böckmann.

Auch stayed in Vaihingen until 1798 when he was hired as a ducal court mechanic (Großherzoglichen Hofmechanicus) at the Weimar court, a prestigious position, that he held until his death in 1842. As court mechanic for the Duke of Weimar, he worked mainly for the new Seeberg Observatory from 1798 on. The renowned astronomer Baron Franz Xaver von Zach headed the observatory until 1806 and was one of Jacob Auch’s most important customers. Auch supplied numerous watches and instruments for the observatory, which was at the time the most modern in Europe.

Auch is well known as the author of two books for watchmaking—Taschenbuch für Uhrenbesitzer (Weimar, 1806) and Handbuch für Landuhrmacher (Weimar, 1827). The latter was published for the first time in 1827 and reprinted many times during the next century.

Besides his calculating machine, Auch is known as a maker of many clocks and chronometers, besides the instruments for the Seeberg Observatory (including a telescope for Johann Wolfgang von Goethe, who visited him in 1799 and 1800). Auch also created important astronomer’s pocket watches in the style of his master Philipp Hahn, with dials on both sides; they showed the traditional watch face on one side and planetaria on the other. To the present day survived a very good double-dial astronomical watch, made by Auch (see the nearby photo).

Jacob Auch died on 20 March 1842, in Weimar. He was inherited by his son, Johann Jacob Auch (1789-1885), who started in 1821 in his father’s workshop in Weimar, and began to build mainly tower clocks according to a completely new functional principle.

In 1770 the Württemberg pastor, astronomer, engineer, and entrepreneur Philipp Matthäus Hahn turned his attention to the creation of calculating machines, devising a simple calculation device (so-called Rechentrommel – calculation drum), then an adding device, and finally a more elaborate cylindrical calculating machine. The first two devices were not so innovative, but Hahn’s cylindrical calculators were the first fully functional popular four-species mechanical calculating machines in the world (the earlier machines of Anton Braun and Jacob Leupold remained relatively obscured and unknown to the public).

Philipp Hahn was a gifted mechanic, who was engaged mainly in making clocks and planetariums. He needed a calculating device, in order to calculate the parameters of his machines, that’s why sometime in the summer of 1770 he started to design several calculating devices. Let’s examine what he devised:

The Calculating Drum of Hahn

It seems the first and simplest calculating device of Hahn was the calculating drum (Rechentrommel), which he devised around 1770. It was a simple calculating device (see the lower photo), with manually rotated inscribed scales, used for adding numbers.

The Cylindrical Calculating Machine of Hahn

The first working copy of Hahn’s most advanced calculating machine, his cylindrical calculator, was ready in 1773, but it was demonstrated as late as 1778 because Hahn has difficulties with the reliability of the tens carry mechanism. Until 1779 four machines were made, till the end of his life, Hahn manufactured about 5-6 devices, two of which still exist in the Württemberg State Museum in Stuttgart and in the Technoseum in Mannheim. After his death, several calculating machines by his design were created by his apprentices, in the photo below you can see a variety of Hahn’s machine, made by Johann Christoph Schuster, an apprentice, and brother-in-law of Hahn.

Hahn certainly has been acquainted with machine of Leibniz (not only from Theatrum arithmetico-geometricum of Leupold, but also from other sources), and that’s probably the reason to use the stepped drum of Leibniz in the construction of his device. However, the arrangement of the device has some similarities not with the Stepped Reckoner of Leibniz, but with the calculating machines of Leupold and Braun.

In an article in the magazine Teutschen Merkur from 1779, Hahn mentioned his inspirator:
When my time was occupied with making astronomical clocks, I had to deal with calculations of long fractions, multiplication, and division of large numbers, and I was so overwhelmed, that my primary work was close to being stopped. Then I recalled that some time ago I read a book for Leibniz, which mentioned his calculating machine, for which he spent a lot of money, without satisfactory results. I decided to spare some time in this direction. Certainly, I also wasted much time and money experimenting and troubleshooting the construction of my device. Finally, I managed to construct a rather advanced and reliable machine. Most difficulties I met during the construction of the tens carrying mechanism.

Hahn needed quite some time to solve the problem with the tens-carry mechanism (he complained several times about the poor quality work of his mechanics), but he managed to resolve it, partly by changing the initial rectangular form of the machine with a circular. So the first working copies of the machine had ten digital positions, and the latter had 12 digital positions.

The main part of the mechanism of each digital position is a small stepped drum (see the staffelwalze in the lower drawing), mounted on an axis, which can be moved upwards and downwards.

During the rotation of the mechanisms of the machine by means of the handle in the middle of the lid, a stepped drum will be engaged with the wheel of the main counter, which is also attached to vertical axes, and according to the vertical position of the appropriate stepped drum, the wheel will be rotated to 0, 1, …, 9 teeth.

The dials are graduated with two scales. The outer ring of digits is black and is used during adding and multiplication, the inner one is red, and is used during subtraction and division. The digits of the inner scale actually are complementing to 9 of those in the outer scale (i.e. below 0 is 9, below 1 is 8, etc.).

The entered in the input mechanism (stepped drums) number is transferred to the main counter by rotating the handler. There is also an additional counter, which counters the revolutions of the handle. The module of the additional and main counter is separated by the calculating module (module with the stepped drums) in a separate ring. This means, that the calculating mechanism is separated by the displaying mechanism. Thus, by rotating the ring of the counters, we actually can move the multiplier (divisor), during the multiplication (division). This moving can be controlled by a special arrow-pointer.

An adding operation can be done as follows:
1. The dials must be set to 0 (if it is necessary). By rotating the axes of the main counter, we set the first addend in the bigger dial (with black digits).
2. Then by pulling the axes of the stepped drums we set another addend.
3. By rotating the handle to 1 revolution, the number is transferred to the main counter and the result can be seen in the windows of the dials.

The subtraction can be performed in a similar way, but the minuend is set according to the red digits, while the subtrahend is set by pulling the axes of the stepped drums. After rotating the handle to one revolution, the result can be seen in the windows of the dials.

The multiplication can be done (by performing successive additions) thus:
1. The dials must be set to 0 (if it is necessary). The multiplicand is set by pulling the axes of the stepped drums.
2. The handle must be rotated to the revolutions, equal to the number of the units of multiplier (the number of revolutions can be seen in the small dials).
3. Then we have to multiply the multiplicand by the tens of the multiplier, so we have to shift the multiplicand one digital position to the left, by rotating the ring with the dials.
4. The handle must be rotated to the revolutions, equal to the number of the tens of multiplier.
5. If it is necessary, the same actions must be repeated for hundreds, thousands… of the multiplier.

The division is done in a way, similar to multiplication, but in this case, are used the red digits of the dials and it is based on successive subtractions.

The calculating machine of Hahn became popular in Germany at the end of the 18th century and was demonstrated to many “celebrities” like Kaiser Joseph II, Johann Wolfgang von Goethe (Goethe visited Hahn in 1779 in his workshop in Kornwestheim), Herzog Carl von Weimar zu Gast, and described in the press.

The Adding Machine of Hahn

It is known also that Hahn designed and manufactured several simple adding machines, which he sold during his lifetime. These devices have been used for monetary calculations (for mechanizing the changeover between Kreuzer and Gulden, where 1 Gulden = 60 Kreuzer). Unfortunately, none of these survived to our time, there is only one copy of a machine, attributed to Hahn, kept now in the collection of Arithmeum Museum, Bonn (see the lower photo).

The adding device in Arithmeum has a brass and steel mechanism, put in a leather-covered wooden box. It has six dials in a row, and the dials are set by means of a stylus. Obviously, only addition is possible, as there is no inscription for complemented to 9 digits. The dials are returned to zero by turning them backward. The tens-carry mechanism is simple but fully functional. Later one of Hahn’s apprentices, Jakob Auch, will create a similar machine, but with an improved tens-carry mechanism.

The construction principles of Hahn’s machines were continued by his eldest son, Christoph Matthäus Hahn (1767-1833), who worked as a court mechanic in Stuttgart, by his apprentices Jakob Auch (1765-1842) and Johann Christoph Schuster (1759-1823, Schuster married one of Hahn’s sisters), by Johann Jakob Sauter (1743-1805, Sauter worked for Hahn in his workshop since 1868 as an assistant for making clocks and balances) and his sons, and by his friend Philipp Gottfried Schaudt.

Biography of Philipp Matthäus Hahn

Already at his lifetime the German vicar Philipp Matthäus Hahn was known in church circles through his theological writings, with princes and nobles by his large astronomical clocks and machines, and the upper middle class through his pocket watches, scales, and calculating machines.

Philipp Matthäus Hahn was born on 25 November 1739, in Scharnhausen auf den Fildern (near Stuttgart), as the second of eight children (Philipp had an elder sister, Juliane Felicitas, b. 18 Feb 1737) in the family of the pastor Georg Gottfried Hahn (b. 18 Oct 1705 Untersielmingen, d. 25 May 1764 Ostdorf) and Juliana Kunigunde Justine Hahn, nee Kaufmann (b. 18 May 1711 Maichingen, d. 26 Feb 1752 Scharnhausen), who married on 8 May, 1736.

Hahns was a rather prominent and wealthy local family, known to live in Scharnhausen since the 16th century. Philipp Matthäus got his name after his grandfathers—Johann Philipp Kaufmann (1661-1748), a pastor from Stuttgart, and Matthäus Hahn (1670-1759), a merchant from Sielmingen auf den Fildern. Juliana Hahn died in February 1752, and in November 1852, Georg Hahn married a second time to Charlotte Dorothea Maichel (b. 6 Feb 1733 Tübingen, d. 7 May 1780 Stuttgart), and the new family had five more children.

As a little boy, Philipp was taught by his father and by his maternal grandfather for four years in ancient languages and religions (Latin, Greek, and Hebrew). Being only 8 y.o. he became interested in astronomical observations and found in his father’s library a book with a description of the celestial sphere, which delighted him for a long time. Two years later, Philipp constructed a simple sundial.

From 1749 to 1754 Philipp attended Latin schools in Esslingen and in Nürtingen, studying religion, but also painting, and especially mathematics. During this time he kept his interest in astronomical observations and sundials and was promoted by Tobias Mayer, the future director of the Göttingen Observatory. In May 1756, the Hahn family moved to Onstmettingen, in the Swabian Jura (in 1755 Georg Hahn was transferred for disciplinary reasons by the consistory there for drunkenness). There Philipp Hahn met his future assistant—the local schoolmaster Philipp Gottfried Schaudt (1739-1809), who had learned the art of watch-making with the local craftsmen—brothers Johannes and Paulus Sauter. This meeting marked the beginning of a lifelong friendship and successful cooperation between the two because Hahn used to use Schaudt’s technical skills to implement his ideas into practice.

On 22 October 1756, Hahn enrolled in the Protestant theological seminary Tübinger Stift in Tübingen to study theology, and there continued his occasions with clocks. (It is amazing, that some 150 years before Hahn, in the same college studied also theology the inventor of the first mechanical calculating machine—canberra dating apps, however Hahn, in contrast to Schickard, later on, will reject the proposed to him professorship there.)

Hahn had a hard time in Tübingen, because his father couldn’t support his children through university. In 1758 Philipp managed to get a two years grant from the Widerholt’s family foundation, and also got some money from his stepmother. In the same 1758 he (for the first time) also had been paid out for his technical knowledge and his mechanical skill—during the semester break, he got thirty guilders to make a sundial for a church. During this period his best friend was Schaudt, as both teenagers shared a pronounced scientific curiosity and technical enthusiasm. Together the young men cut glass, and built mouthpieces, telescopes, microscopes, and sundials. When Hahn was able to spend the lecture-free periods in Onstmettingen, the two friends sat together all night, dismantling clocks, building mechanical equipment, and watching the starry sky.

In 1760 Hahn obtained a Master’s degree in Philosophy in Tübingen, then worked for about a year as a private teacher in the Benedictine monastery in Lorch in Lorch bei Schwäbisch Gmünd. At that time Hahn worked on the construction of a Perpetuum Mobile, but soon he realized it is impossible to build such a machine. In 1761 Hahn started his way in Church as a Vicar, then moved to Herrenberg (the hometown of canberra dating apps), to receive in 1764 a Vicariate in Onstmettingen, succeeding his father, who had died suddenly. There he (together with his old friend and local schoolmaster Schaudt) organized a workshop for the construction of scales, astronomical clocks, and machines to glory of God.

In 1766 Hahn designed, and in 1667 Schaudt constructed a big brass and iron astronomical clock, presented to Duke Karl Eugen, the Herzog of Württemberg, who admired the inventor (he later became his patron and used to dub Hahn as “the watchmaker God”), gave him a reward of 300 guilders (quite a sum for the time), and promptly ordered a larger machine for the Library of Ludwigsburg (this device, known as Astronomic World Machine, now stands in the Stuttgart Landesmuseum). In Onstmettingen Hahn constructed also many solar, steeple, pocket and pendant watches, and invented a new type of weightless balance—the pendulum balance.

On 24 May 1764, Philipp Hahn married 15 y.o. Anna Maria Rapp (1749-1775), a daughter of the mayor of Schorndorf Ulrich Rapp. The family had six sons, but two of them died as babies, so left four—Christoph Matthäus (1767-1833), Christian Gottfried (1769-1831), Gottlieb Friedrich (1771-1802), and Immanuel (1773-1833). All the sons shared Hahn’s interests in mechanics and mathematics, and two of them—Christof Matthäus and Christian Gottfried also became skillful watchmakers.

In 1770 Duke Karl Eugen proposed a mathematics professorship at Tübingen to Hahn, but he refused it (he still needed to be in the bosom of the church.) In the same 1770 however, Hahn accepted another position, arranged by the Duke, and in March moved to serve in the well-paid parish Kornwestheim, where he lived in the new rectory (see the upper photo) and arranged a large workshop, where he invited to work his brothers—Georg David Polykarp (1747-1814) and Ägidius Stephanus Gottfried (1749-1827). There unfortunately his wife Anna died too young, on 10 July 1775, giving birth to their seventh child. In 1776 Hahn married a second time to Beate Regine Flattich (1757-1824), a daughter of the Münchinger parson Johann Friedrich Flattich (1713-1797). The new family had eight children.

In June 1779 Hahn was appointed as a member of the Erfurt Academy of Sciences. In 1781 Duke Karl Eugen again arranged a new profitable position for Hahn, in the best-paid parish in the whole country, Echterdingen, near Stuttgart. In Echterdingen Hahn dealt mainly with pocket watches and even wrote a treatise in this regard.

In 1772-1774 Hahn published several theological books: The main cause of the Apocalypse (1772), Clue to the understanding of the Kingdom of God (1774), and two sermon books. The printing of books he financed from the profits, which dropped from the workshop. So does the technical work of Hahn was indirectly working for the kingdom of God:-) Hahn certainly published also several technical books: Beschreibung mechanischer Kunstwerke in 1774, and Von Verbesserung der Taschenuhren in 1784.

Philipp Matthäus Hahn had a tireless nature. A working day of 16 to 18 hours was the norm for him, despite suffering most of his life from a stomach illness. He was a pedantic boss, both in his workshop and in the house. This remarkable man died of lung disease (pneumonia or lung cancer) on 2 May 1790, in Echterdingen, and was buried in Kirchfriedhof von Echterdingen.

In April 1886, Eduard Selling, a professor of mathematics and astronomy at the University of Würzburg, Germany, received a patent for a calculating machine with a very interesting construction.

The driving force behind this invention was (as usual) the personal need for a better calculating tool. It’s known that since 1877 Selling had been commissioned by various ministries dealing with actuarial matters, especially on the revision of the pension system in Bavaria. For his extensive mathematical calculations, he used a calculating machine of Thomas de Colmar, with which he was not satisfied. That’s why, he decided to create his own entirely different machine, not only suitable for multiplication but also to be offered at a lower price and to avoid all the drawbacks of Thomas’ machine.

The first variant of the device was patented in 1886 (Deutsches Reichs-Patent №39634, 16 April 1886), later on, Selling received three more patents in Germany for improvements of his machine, as well as patents in Austria (pat. №31289 and №20923), Belgium (№74104), Switzerland (№31942), France (№175412), England (№8912 and №23737), Italy (№20326), and USA (see patent http://www.computer-timeline.com/fester-dating-site/). The machine was described also in his book dating apps for handicapped, Berlin, Springer, 1887.

The calculating machine of Selling has two main variants (let’s call them the first machine and the second machine). It was put in production, although in small quantities (some 30-40 machines were produced until the production ended in 1898), by the Workshop for Precision Mechanics of Max Ott, in Munich. The price was 400 marks. The machine of Selling was awarded at the Columbian Exposition (also known as the Chicago World’s Fair) in 1893.

In the construction of the machine took part the teenage son of a friend of Selling—the future genius of mechanic calculating machines, Christel Hamann.

The internal mechanism of the machine is based on the so-called Nürnberger Schere (a popular children’s toy at this time), in English, this mechanism is called Nuremberg scissors or lazy-tongs (see the patent drawing below).

The machine is 35 cm wide, 40 cm long, and 15 cm high.

The multiplicand digits must be entered in a representation that differs from the decimal system, e.g. 18 must be represented as 20-2, although the result is shown in the decimal system.

The calculating wheels of a regular calculating machine (which transfers the motion to the digital wheels) are replaced by lazy-tongs. To the joints of these the ends of racks are pinned, and as they are stretched out the racks are moved forward 0 to 9 steps, according to the joints they are pinned to. The racks gear directly in the digital wheels and the figures are placed on cylinders. The carrying is done continuously by a train of epicycloidal wheels. The working is thus rendered very smooth, without the jerks that the ordinary carrying tooth produces; but the arrangement has the disadvantage that the resulting figures do not appear in a straight line, a figure followed by a 5, for instance, is already carried half a step forward. This is not a serious matter in the hands of a mathematician or an operator using the machine constantly, but it is serious for casual work. Anyhow, it has prevented the machine from being a commercial success. Actually, this was the second machine with continuous tens carry, after the calculating machine of Chebyshev. For ease and rapidity of working it surpasses all other machines. Since the lazy-tongs allow an extension equivalent to five turnings of the handle if the multiplier is 5 or under, one push forward will do the same as five (or fewer) turns of the handle, and more than two pushes are never required.

Obviously, the problem of tens carry was solved in a new, albeit very complex, way. Moreover, besides the vulnerability of the tens carry mechanism, other parts of the machine also have complications. That’s why Selling tried to improve the mechanism in his second machine (see the photo below), although without great success.

In one of his German patents (№88297 from 1894), Selling attempted to design an electric calculating machine (with no engine, but through contacts and electromagnets), but apparently without success.

The calculating machines of Eduard Selling demonstrated exceptional ideas and ingenuity but were fragile, complex, and difficult to manufacture and work, that’s why they didn’t achieve any market success.

Biography of Eduard Selling

Eduard Selling was born on 5 November 1834, in Ansbach, Bavaria, Germany, in a family of a professor. He studied mathematics at Georg-August-Universität in Göttingen and Ludwig-Maximilians-Universität in München, where he was a student of the famous German mathematician and astronomer Philipp Ludwig Ritter von Seidel.

In 1859 Selling obtained a Ph.D. degree in mathematics at Universität München (with a thesis on prime numbers, under the supervision of Bernhard Riemann), and in 1860 he was appointed as an associate professor (professor extraordinarius) of mathematics at the Bayerische Julius-Maximilians-Universität in Würzburg, recommended by the famous mathematician Leopold Kronecker. Selling held this position and taught mathematics and astronomy until his retirement in 1906.

In 1873 Selling wrote an important paper on binary and ternary quadratic forms which was also translated into French and cited by Henri Poincaré, Émile Picard, and Paul Gustav Heinrich Bachmann. In 1879 Selling was appointed as a curator of the Astronomical Institute. He proved himself as a very good mathematician and published a series of works on number theory and then on insurance mathematics. On behalf of various ministries, he developed models, with which the pension system in Bavaria could be rearranged.

Eduard Selling died on 31 January 1920, in München.

The prominent German Jesuit polymath Athanasius Kircher, whose interests covered “everything under the sun”, has a significant place in this site, because of his version of the Llullistic method, his automata, and his calculating tool Organum Mathematicum. Let’s see what is his contribution in the area of computing.

*** Kircher’s Llullistic method ***

Kircher was a professor of mathematics at the Roman college until 1646, and when he was released from teaching duties, he started publishing books, concentrating on a different subject every three to four years. He received visits or letters from scientists, royalty and clergy from all over Europe and beyond, together with a multitude of artifacts, curiosities of natural history and mechanical apparatus. These, together with his huge library, he later donated to a museum, which eventually became the famous museum of the Roman College or the Museum Kircherianum. This museum became one of the top attractions of Rome in the 17th century and continued to exist up to 1915.

Interestingly for us, in 1669 Kircher published in Amsterdam a book, named Ars Magna Sciendi, Sive Combinatoria (see the nearby lower).

In the third chapter of his book, Kircher presented a new and universal version of the Llullistic method of a combination of notions. Kircher seems to be convinced that the Llullistic art of combination is a secret and mystical matter, some kind of esoteric doctrine.

Kircher used the same circle-figures of Llull, but the alphabet which Kircher proposes as material for his combination-machine reveals the difference from Lullus’ at first sight (see the figure below). It is not the signification in correlation with the position in the table, because all nine places in each table are filled with the same significations we find in the Llullistic tables, which makes the difference. It is the notation, which creates the difference.

In contrast with Llull, who used Latin words, with clearly defined significations for his combinations, Kircher began filling the tables with signs and symbols of a different kind. This means, that he attempted to solve problems other than the demonstration of the truth, which the Catholic Church had claimed.

Furthermore, as can be seen from the following figure, Kircher tried to calculate the possible combinations of all limited alphabets (not only graphical but also mathematical). As it is known, that at that time Kircher was a grand master of decipherment and tried to translate Egyptian hieroglyphic texts, it is clear that this schema can be connected to the process of encoding and decoding. Regarding his tabula generalis, the more mathematical way of thinking created the great difference between Llull and Kircher.

Kircher consequently published a book about the problems of encoding and decoding, and he even designed mechanical machines for the task.

*** Kircher’s Automata ***

Athanasius Kircher was notable for his interest in machines and automata of different kinds: optical and acoustic machines, music boxes, hydraulic and astronomical machines, clockworks, tools and toys, mechanical puppets, and so on. This collection will become a foundation for the famous Musaeum Kircherianum. He also had plans for building a talking head and mechanical music-makers. There is a note from the British physician Edward Browne (1644-1708) who arrived in Rome in the 1670s to visit Kircher, and saw his closett of rarieties, which included a perpetual motion machine and a talking head. Kircher wanted to create a speaking statue for the visit of Queen Christina of Sweden to the Musaeum Kircherianum, a statue that will have to answer the questions that it is asked.

Obviously the Kircher’s interests in the field of automata began much earlier. In his book Magne sive de Arte Magnetica (see the upper title page), published for the first time in 1641, he describes and illustrates several automata, which depend for their action upon magnetism and pneumatics.

In Magne sive de Arte Magnetica Kircher gives a representation of an old automaton, commonly attributed to the Greek scientist Archytas of Tarentum (BC 428-BC 347) (who is believed to be the founder of mathematical mechanics and alleged inventor of the screw and the pulley), so-called Dove of Archytas. It was reputed to be the first artificial, self-propelled flying device, set in motion by a jet of what was probably steam, said to have actually flown some 200 meters. According to another story, the Dove was put in action by a revolving loadstone and was made to fly around a dial and mark the hours by pointing to the figures on its edge.

On the lower illustration can be seen a wheel, driven by 2 Eolipiles in the form of human heads, which blow out jets of steam against the cellular periphery of the wheel. The little boilers (marked C and D), hidden in the heads, are illustrated in the lower part of the page.

Athanasius Kircher was also one of the first people, who described the mechanical organ utilizing the pinned barrel (although the hydraulic organ had been well-known since the time of Ctesibius). Kircher described also “the automatic organ machine which utters the voices of animals and birds” in which a satyr played a short piece on the pan pipes, to which a nymph replied, like an echo, with a melody played upon a small organ.

Kircher also devised a hydraulic machine to represent the Resurrection of the Savior and another device to exhibit Christ walking on water, and bringing help to Peter who is gradually sinking, by a magnetic trick. This device featured a strong magnet placed in Peter’s chest and the steel out of which were wrought Christ’s outstretched hands or any part of his toga turned toward Peter. The two figures, propped on corks in a pool of water, would then be drawn inexorably together: the iron hands of Christ soon feel the magnetic power diffused from the breast of Peter. The artifice will be greater if the statue of Christ is flexible in its middle, for in this way it will bend itself, to the great admiration and piety of the spectators.

*** Kircher’s Organum Mathematicum ***

In late 1650s as a prominent mathematician Athanasius Kircher was asked to prepare a set of mathematical tools for teaching the young Austrian crown prince (Archduke) Karl Joseph Erzherzog von Österreich (1649-1664). The order was fulfilled and a set of ten different tools of bone-like tablets for performing a variety of different tasks was manufactured (see the nearby image of the tool, placed now in the Istituto e museo di storia della scienza, Florence, Italy) and sent to Archduke in 1661, who was very pleased. The toolset (called Organum Mathematicum, Mathematische Orgel or cista) was placed in a veneered wooden chest with a hinged lid (taking up the space of a large desk) and was described later in a book by his pupil and friend Gaspar Schott (1608-1666)—Organum Mathematicum libris IX explicatum, published in 1668 in Würzburg, Germany.

Schott not only described Kircher’s Organum Mathematicum, but added his own improvement to Napier’s reckoning rods (he most probably didn’t know for the Rechenuhr of Schickard, created in the early 1620s, which also used rods, places on a cylinder’s surface). Instead of having to deal with a number of individual little rods each time one desired to perform multiplication, Schott designed a box (cistula) in which Napier’s rods were converted into cylinders, each one of them incorporating the complete set of multiples from one to nine previously found on several separate rods. To operate the machine, one only had to turn the cylinders’ handles to the proper figure needed to be multiplied, and it then only became a matter of following Napier’s well-defined rules of rabdology. Moreover, to ensure the machine would be utilized by the greatest possible number of people, a table of addition and subtraction was provided on the inside cover of the box.

Later on, the multiplication tool from Organum Mathematicum (with an improvement of Schott) was described in Theatrum arithmetico-geometricum of Leupold. The arithmetic tool consists of ten cylinders, on which surface are placed strips with inscribed Napier’s rods. The cylinders (see the lower figure) are mounted in a box, which is closed to the upper side from a lined sheet of pasteboard with narrow vertical slits. From the front side of the box are placed handles, attached to the cylinders, which can be used for rotating the cylinders, thus can be set needed multiplicand on the rods. On the inner side of the hinged lid of the box is inscribed an addition table to aid the operator.

Biography of Athanasius Kircher

Athanasius Kircher was born at three in the morning on 2 May (on the feast day of St. Athanasius, hence his name), 1601 (or 1602, even though he was unsure for the year), in Geisa, a small town located 26 km northeast of Fulda, Germany.

Athanasius was the seventh (last and weakest) child and fourth son of Johann (Johannes) Kircher of Mainz and Anna (nee Gansek), daughter of a burgher from Fulda. In fact, the family had nine children (six sons and three daughters, Ana, Agnes, and Eva), but two of the boys died in infancy, and the other four (Johannes, Andreas, Joachim, and Athanasius) entered various religious orders.

Johann Kircher, the father of Athanasius, had studied philosophy and theology at Mainz, receiving a doctorate in theology. He was called first by the Benedictine house at Seligenstadt to be a professor of theology. Afterward, in the early 1570s, he was called by the Prince-Abbot Balthasar of Fulda, who named him adviser and Amstvogt (bailiff) of Haselstein, one of the administrative divisions of Fulda. Johann Kircher administered affairs and justice for the Prince-Abbot until 1579, and during this period he met and married Anna Gansek, the virtuous daughter of one of Fulda’s most respected inhabitants. Thereafter he moved with his family to Geisa, where he served a two-year period as Stadtschultheiss (mayor) before dedicating himself to scholarship, teaching, and raising his children, declining all subsequent offers for political positions.

Athanasius received his early education mostly from his father (music, Latin, and mathematics) and private tutors (e.g. his father hired a local rabbi to teach him Hebrew), but also visited the Dame school in Geisa. At the age of ten, he was sent in the footsteps of his brothers to the Papal Seminary in Fulda. Before he left at the age of 16, he had learned Latin, Greek, and Hebrew, and presumably at some point had made the lifetime commitment to a monastic career.

By this time, Kircher had developed into a quiet, introspective youth, suspected by his teachers of backwardness and slowness to respond to questions and commands. Unfortunately, he had quite a few personal troubles during his childhood. As a boy, he escaped serious injury or death at least three times: once while swimming he was sucked beneath the moving mill-wheel; secondly, he was jostled beneath the hooves of a phalanx of horse-riders; thirdly, he lost his way in the forests of the Spessart and wandered a whole day, before to stumble across some harvesters, who helped him. While Kircher emerged untouched from each of these accidents, in January 1617, while skating, he fell awkwardly, sustaining a serious abdominal hernia. Shortly before this, an ulcer had broken out of his leg, caused by protracted cold during winter evenings when he studied and meditated.

After failing in his first application, to the Jesuit College in Mainz, he was admitted as a novice to the college at Paderborn in October 1618. In Paderborn Kircher studied humanities, natural science, and mathematics, but in the early 1620s, his education was interrupted by the onset of the Thirty Years War. The advance of the fiercely anti-Jesuit army prompted him, with two companions, to flee at the end of January 1622. They struggled for many days through deep snow, penniless and begging for their food, and proceeded to cross the frozen Rhine river. Halfway across, a piece of ice broke loose and Kircher was carried away on it. His companions expected never to see him again. But he succeeded in swimming through the freezing water to the bank, and walking for three hours until he reached a shelter.

Kircher continued his education in philosophy, physics, and natural sciences at Cologne and in 1623, at Koblenz, where he took up humanities and languages. In 1624, at Heiligenstadt, he studied languages and “physical curiosities.” In 1625-1628, he studied theology, oriental languages, and astronomy at the Jesuit College in Mainz, where he obtained a doctorate in theology. While still a student, he taught to support himself. At Koblenz (1623), he taught Greek, at Heiligenstadt (1624), he taught grammar, and at Mainz, he taught Greek and conducted the choir.

In 1628 he was ordained within the Jesuit order and admitted to the fourth vow, and he finished his last year of probation at Speier, when the chair of ethics and mathematics was given to him at the University of Würzburg, while at the same time he had to give instructions in the Syrian and Hebrew languages. However, the disorders consequent from the Thirty Years’ War (1618–1648) forced him to go first to Lyons in France (1631) and later to Avignon, where he taught mathematics, natural philosophy, and oriental languages at the Jesuit college at Avignon. Here Kircher installed an astronomic observatory and an elaborate planetarium that showed the position of the Sun, Moon, and planets by means of a complex system of mirrors. The planetarium became a popular attraction in the city.

In 1632, the Holy Roman Emperor Ferdinand II appointed him to the professorship of mathematics at Vienna or the position of court mathematician (to replace Johannes Kepler as court mathematician in the Hapsburg dynasty), but Pope Urban VIII and Cardinal Barberini quickly offered him a position in Rome so that he would not go. At the beginning of 1634, Kircher was appointed professor of mathematics, physics, and oriental languages at the Collegio Romano (now the Pontifical Gregorian University). He resigned after 8 years and returned to independent studies, undertaking such independent studies for 46 years of his life. He was supported in Rome by the Papal as well as another patronage.

In 1656, the Black Plague swept across Western Europe and Italy, and Kircher spent most of his time nursing the ill and attempting to find a cure. He examined the blood of his patients through a microscope and thought that the plague was caused by vernimuli in the blood. What he might well have seen was large bacteria in the contaminated blood specimens rather than the much smaller plague bacillus (Yersinia pestis). Despite this error, Kircher’s work is notable as the first attempt to apply the microscope to find the cause of disease and the first mention of a germ theory.

Kircher was not only a brilliant scientist but also a “business-oriented” and very influential man. He is one of the first scientists who was able to command support through the sale of his works. In 1661 he sold exclusive rights to publish his books (he was a prolific writer with 32 books and some 23 manuscripts of works that were not published) to the prominent Dutch publisher Janssonius for a large sum of money. Kircher apparently understood the patronage game very well, let’s mention only some of his patrons—popes Urban VIII and Alexander VII, Holy Roman Emperors Ferdinand II and Ferdinand III, Christina, Queen of Sweden, etc. For example his books on magnetism (1640) and the Egyptian language (1643) he dedicated to Emperor Ferdinand III, who not only paid for the printing of his books but also granted Kircher a pension.

In 1651, Kircher was assigned to organize the collections of objects of different types which belonged to the Roman College. He established a museum in one of the rooms of the college which was soon known as the Museum Kircherianum. The collection contained archaeological objects of Roman and Etruscan origin, given in great part by the Italian aristocrat Alfonso Donnino. It included also archaeological pieces from ancient Egypt, such as obelisks and mummies, and curiosities brought by Jesuit missionaries from all parts of the world. Another section was formed of minerals, rocks, fossils, and strange stuffed animals and skeletons. The museum also contained an art gallery with paintings and statues. Kircher added a collection of 19 machines and instruments built by himself for his experiments and described them in his books. This formed the most remarkable part of the museum. Among them, there was an automatic organ that imitated the songs of birds, a magic lantern (Laterna magica) to project images, and other instruments used for hydraulics, optical and acoustic experiments. Some instruments were of statues, with spiral tubes in their interior that seemed to talk. One of these acoustic tubes connected the museum with the porter’s lodge to announce visitors.

Athanasius Kircher died in Rome on 27 November 1680 and was buried in the Church of the Gesù. This fascinating figure left behind numerous manuscripts, notebooks, and a voluminous backlog of correspondence, much of which was published piecemeal over the following decades. Among some 760 addressees of his letters are to be found four popes, two emperors, the kings of France and Spain, the Queen of Sweden, cardinals, bishops, members of the European nobility, scholars, and Jesuit companions. Among the scientists, one finds Cassini, Mersenne, Huygens, Leibniz, and Gassendi.

Although Athanasius Kircher is known for a number of innovations, the vast majority of his output consisted of compilations of already-known material. His interests ranged widely over both the humanities and the sciences, and his most significant contribution was in the dissemination of this knowledge.

In the July 1751 issue of the earliest scientific journal in Europe—the french Le Journal des Sçavans, was published a description of Machine Arithmétique of Jacob-Rodrigues Pereire. The device was initially made as an aid for deaf and mute people (Pereire is known as the first teacher of deaf-mutes in France), but the inventor mentioned that it is very useful not only for mute children, but for all those wishing to learn the science of numbers.

The Arithmetical Machine of Pereire is a simple adding device with a mechanism quite similar and inspired by Abaque Rhabdologique of Claude Perrault, but was more complex. The device is enclosed in a small box approximately three inches long, its constriction consists of coaxial wheels, and it was built in a very modular way, with no auxiliary wheels and no gears. At least one example has been manufactured, and Pereire donated it to a friend—the famous french statesman Baron Jacques Necker (1732—1804), who used it for personal calculations. Unfortunately, the device didn’t survive to the present day, so we have to limit our research to the elaborate description in the journal. Here it is (Excerpt from the register of the Royal Academy of Sciences, 5 May 1751, translated by Cris Stenella):

We have examined on the orders of the Academy an Arithmetical machine, presented by Mr. Pereire, of whom the Company has already approved the method of teaching speech to mutes.

Mr. Pereire cites in the paper he read to the Academy on the 16th of last December, everything currently known about machines of this kind, among which those by Mrs. Pascal, Perrault, Lépine, and Boistissandeau are the best-known. The first and two last take up a somewhat embarrassing volume and consist of many wheels, springs, ratchets, and other parts which make them costly, subject to repair, and inconvenient in use.

The rabdological abacus of Mr. Perrault is much simpler, and it is this instrument that the machine of Mr. Pereire resembles most. The abacus is composed of small rulers, each containing two columns of numbers, one on top of the other, separated by an empty space. The numbers in the first column are along the order 0, 1, 2, 3, etc. until 9 and those in the second column are in the reverse order, 9, 8, 7, etc. until 0, and the operation is by shifting the rulers in the grooves that contain them. Once they arrive at the bottom end of their travel, a ratchet that is built into the body of the ruler finds an opening for engaging in a groove in the neighboring ruler, making it advance by one step to mark tens of units for the first ruler, and if the ruler arrives at the bottom of its travel and thus indicates no number in the bottom window, one makes the ruler move up until the pointer that is moving it stops at the top of its groove—thus one finds at the bottom window the units that accompany the ten that the ratchet has been made to indicate, as will be explained more thoroughly in describing the use of this instrument.

Instead of putting the two columns on top of each other on each slide, Mr. Perrault could have put them side by side, in putting one slightly higher than the other, and placing the indicator windows in which the numbers appear conveniently accordingly. In this way, the abacus would have no more need for such a substantial length.

The machine of Mr. Pereire adopts this idea but is more ingenious.

Instead of rulers, it uses small wooden wheels or very short cylinders, like trictrac stones, all put on a common axle. The cylindrical surfaces of these stones or wheels thus become rods without end: he has divided the circumference of each of the wheels into thirty equal parts where he has written two series of numbers: the first contains three times the numbers 1 2 3 4 5 6 7 8 9 0, the second one three times the numbers 0 9 8 7 6 5 4 3 2 1. Of these wheels, there is one for the “Deniers”, one for the “Sols”, one for the simplest fractions like 1/2, 1/3, 1/4, 1/6, etc. and seven for the whole numbers, units, tens, hundreds, thousands, etc. until millions: and all these wheels together form but one cylinder three inches long to 18 eights in diameter, enclosed in a small trunk-shaped box.

There are on top of this box as many grooves as there are wheels, each occupying one-third of the circumference of the cylinder, by which one makes the wheels turn with the tip of a stylus, in the same way, one makes Mr. Perrault’s abacus’ rods move, taking the number one wants from 1 to 9 and 0, with this advantage that here the columns of numbers follow each other without interruption, one is never obliged to make the wheels turn back to make the number which results from the operation one makes, appear, as Perrault´s abacus often requires.

Mr. Pereire has divided the circumference of the wheel into thirty parts as opposed to twenty, so that the slits which are on top of the box would occupy only one-third of the circumference of the circle, instead of half, which would not have been as convenient. He could have divided them into forty or fifty parts as well, and then the slits would have taken only 1/4th or 1/5th part of the circle circumference, but this larger number of divisions would have necessitated making the wheels larger.

Additionally, on top of the box which contains the wheels, there are two rows of windows along the length of the box, one on the front, and one on the back, those here to find the sum or the product of the numbers one wishes to add or multiply, those there to dial the number from which one wants to subtract, or which one wants to divide by another. The means that Mr. Pereire has found to advance a wheel every time the preceding one passes 10 is very ingenious. For this, along one of the flat sides of each wheel, he has made thirty teeth representing more or less the teeth of a cog wheel. The other face is reserved to place a small balance, made hooked on one side, and along an inclined plane on the other. Each time ten divisions of this wheel have passed, the inclined plane meets a tooth fixed on the iron plate between the two wheels. This tooth forces the balance to move into the body of the wheel, thus pushing out the hook of which the other side consists, through the iron plate, which has an opening, especially for this purpose, hooking behind one of the thirty teeth on the flat side of the neighboring wheel, and making it advance one step. This step made, the inclined plane now being past the tooth on the iron plate, is tilted back into its place by means of a spring, the hook thus returns to the body of the wheel and retracts from the neighboring wheel after having made it move by the value of one tooth.

This entire arrangement seems well-thought-out to us, simple and convenient, and we judge it to be worthy of approval and inclusion in the array of machines approved by the academy.

This all having been said, there are only two things left that we believe would be good to draw the attention of our readers to:

1. By means of the arithmetic machine by Mr. Pereire, one can do without the help of pen and paper, the four arithmetic operations, the first two in pounds, shillings, and pences, and the seven kinds of fractions. This last peculiarity of the machine by Mr. Pereire, which is also unique about it, is all the more useful as one can add or subtract fractions of different denominators with the same ease as if operating on whole numbers: one will find for example that 1/4 1/3 3/8 5/24 makes 1 1/16 and when 5/12 is subtracted, 3/4 remain.

2. That the machine of Mr. Pereire, of which the volume is indicated above, should not be of considerable price, but nevertheless that those willing to procure the machine should advertise Mr. Pereire, as the price could even be lower as the number procured is larger. It is of little surprise that the mechanical arts will be happy to have this new machine, which by itself is very suitable for raising interest, and which is very useful not only for mute children but for all those wishing to learn the science of numbers.
*** End of excerpt from Journal des Sçavans, July 1751 ***

An attempt for the reconstruction of Pereire’s device was made by Mr. Stephan Weiss, you can find the full description on his site—www.mechrech.info. According to Mr. Weiss, the front panel of the device was something like:

Biography of Jacob-Rodrigues Pereira

Jacob-Rodrigues Pereira, better known as Pereire, was born in Berlanga, Extremadura, Spain (or in Peniche, Portugal, according to other sources) on 11 April 1715. He was a descendant of a Marrano family (Marranos were Jews living in Iberia, who converted or were forced to convert to Christianity yet continued to practice Judaism in secret).

Jacob (he was actually baptized with the name of Francisco António Rodrigues) was the seventh of nine children of Sephardi Jews—João Lopes Dias (Abraham Rodrigues) Pereira (1675-1735) and Leonor Ribea Henriques Pereira (1676-1751), native from Chacim, a village in Trás-os-Montes province of Portugal.

In April 1699, his parents with a group of new Christians from Trás-os-Montes (most of them were their relatives), decided to flee from Portugal and the Inquisition, and tried to board a ship to Livorno, Italy (on the board, besides João Lopes Dias and his pregnant wife Leonor, were his father André Rodrigues, his mother Ana Lopes, his three aunts Francisca, Beatriz and Ana, and his two daughters, Branca and Mariana, aged 2 and 3). However, the group was arrested in Cadiz at the order of the Seville Inquisition and all adults were punished with more or less harsh sentences.

On 2 June 1699, still in prison, Leonor gave birth to a boy named Paulino. After a more severe period of punishment, João Lopes Dias has been allowed to reorganize his family life, and the couple had six more children: Beatriz Maria (b. 30 Oct. 1707), Manuel (b. 23 Oct. 1710), Isabel (b. 22 Nov. 1713), Francisco António (b. 11 April 1715), André (b. 6 Oct. 1717), and Luis (b. 2 July 1720). The family lived in several places in Spain, like Berlanga and Llerena, and eventually returned to Portugal in the 1730s, where João Lopes Dias died in Moita in 1735.

It seems Pereira’s family problems with church authorities in Portugal persisted, because in 1741 to escape the charge of heresy Francisco and Leonor emigrated to France, settling initially in Bordeaux. In France, Pereira family returned openly to Judaism, as Francisco adopted the name Jacob, and his mother became Abigail Rivka Rodrigues Pereira (she died in France on 18 Nov. 1751). A lifelong devotee to the well-being of the Jews of southern France, Portugal, and Spain, he was the syndic, or lay leader, of the Sephardi Jewish community of Paris In 1753 Pereira was chosen for Agent of the Portuguese Jews of Bordeaux and in 1760 for Agent of the Portuguese Jews of Paris. In 1777, his efforts led to Portuguese Jews receiving the right to settle in France.

According to the legend, one of the sisters of Jacob-Rodrigues Pereire was deaf and dumb, and trying to communicate with her, he formulated signs for numbers and punctuation. After ten years of study of anatomy and physiology and numerous experiments on congenital deaf-mutes, Pereire received on 19 January 1747, the first testimonial for his labors from the Royal Academy of Belles-Lettres of Caen. Later on, he adapted Juan Pablo Bonet’s manual alphabet by adding 30 hand shapes each corresponding to a sound instead of to a letter.

In 1746 a wealthy French family, the d’Etavignys, hired Pereire to instruct their son. He taught the boy to speak through his method of finger-spelling, called dactylology. In 1749 he set forth his system in a memoir before the Royal Academy of Sciences in Paris. Pereire was well compensated by this family and another who hired him and dismissed Epee’s methods when it became known. His remarkable achievement was even presented to the King of France, Louis XV, who granted him 800 pounds as a mark of esteem. Pereira’s book on the subject, Observations sur les Sourds et Muets, was published by the Académie Royale des Sciences in 1778.

The memoir read before the Academy on the arithmetical machine that he had invented brought him a pension of 800 pounds annually from the King (26 October 1751), while in 1753 he received an honorable mention at a conference held by the Academy to determine the most advantageous methods of supplementing the action of the wind on large sailing vessels. In 1759 the Royal Society of London made Pereire a member, and in 1765 he was appointed royal interpreter of King Louis XV for Spanish and Portuguese.

Pereire took his method with him to the grave when he died in 1780. He is therefore seen as one of the inventors of manual language for the deaf and is credited with being the first person to teach a non-verbal deaf person to speak.

On 5 November 1766, Pereire married his kinswoman Miryam Lopes Dias, then only 19 years old. They had six children, but four died in infancy, and only two survived—Isaac (b. October 1767), and Abigail (b. 1768). Isaac Pereire became a merchant and died early, on 20 Nov. 1806, at the age of 38, but he left three children, two of whom became prominent financiers in Paris: Jacob-Emile Pereire and Isaac Pereire.

Besides his interests in mathematics and physics, Pereire had a thorough knowledge of ancient and modern languages. In 1772, he published a Tahitian vocabulary for Louis-Antoine de Bougainville’s voyage, after learning the language from Ahutoru, the first Tahitian to sail aboard a European vessel. Pereire successfully handled financial matters and discussed with Baron Necker how to restore order in the finances of France.

Jacob-Rodrigues Pereire died in Paris, on 15 September 1780, and was buried in Cimetière de la Villette (in 1876 his remains were transferred to the cemetery of Montmartre). His widow Miriam Lopes Dias moved to Bordeaux with their children, and died there in 1791, at the age of 44. In Bordeaux the street Rodrigues-Pereire was named in his honor.

Jacob’s grandsons, the Péreire brothers (see the nearby image)—Jacob Rodrigue Émile Péreire (1800-1875), and Isaac Péreire (1806-1880), were well-known French financiers and bankers during the second empire, whosе activity in the promotion and organization of railroads in Europe was extraordinary (in 1835 they built the first railway in France, that from Paris to St.-Germain). In 1852, they founded the Société Générale du Crédit Mobilier, one of the most important financial institutions in the world during the mid-19th century. Today in Paris there is Boulevard Pereire, and a metro station Pereire, named after the brothers.

In 1735 Christian Ludwig Gersten (1701-1762), a professor of mathematics at the University of Gießen, traveled to London, to be elected a fellow of the Royal Society and to present to the Society his project of an arithmetical machine. In his description, he claims, that the machine had been designed 12 or 13 years before, most probably in 1722.

The machine was described in the scientific journal Philosophical Transactions of the Royal Society Nr. 438 for the months of July, August, and September 1735 (pages 79–97). In his 19-page detailed presentation, named Description and Use of an Arithmetical Machine… (see description of the machine of Gersten) Gersten mentioned, that he has been acquainted with the machines of Morland, Leibniz, Poleni, and Leupold, and learned that Charles Pascal invented one, and was inspired from them (especially from Leibniz) to create his own calculating device.

The first prototype of the machine was wooden, and after the device had been shewed to some Patrons and Friends of Gersten, they encouraged him to continue the development. The second copy was made from brass and at the end of 1725, Gersten presented it to the Landgrave of Hessen Darmstadt Ludwig V and his son, Prince Georg II (who became Landgrave in 1726). The Landgrave admired the inventor and encouraged him to try to popularize it. Besides the presentation to the English Royal Society, the description of the machine was sent and approved by the French Academie Royale des Sciences, and in 1735 the description was published in the first book of six volume set of Jean Gaffin Gallon—Machines et inventions approuvées par l’Academie Royale des Sciences, depuis son établissment jusqu’a présent; avec leur description.

In 1736 a copy (probably the only prototype) of the machine of Gersten was donated to the Landgrave of Hesse-Darmstadt and was kept in the Castle of Darmstadt until WWII (see the first figure), when it was destroyed by bombs in 1943.  Fortunately, to the present day managed to survive a replica of the device from 1920, made by order of Dr. Franz Trinks, the founder of Rechenmaschinenfabrikation in Braunschweig which is preserved in the Braunschweigisches Landesmuseum (see the third figure).

Let’s examine the arrangement of the machine in the sketch from the presentation to the Royal Society (see the sketch in the second figure).

The dimensions of the machine are—36 cm in width, 37 cm in height, and 7 cm in thickness. It has a six positional input mechanism and seven positional display mechanism (from the design of the machine is evident, that it can be easily extended with additional positional modules). In part 1 of the upper figure are shown the first three digital positions—for units (marked with AA), for tens (marked with BB), and for hundreds (CC). Every position has two sliders, the first of them (the upper one) Gersten named operator, the second one—determinator. The determinator indicates what number will be entered in the calculating mechanism, while the entering is done by moving the operator.

The main element in the calculating mechanism of the machine are ratchet-wheels. They are used in the digital dials for entering numbers, and for tens carry during the calculations.

At the end of his presentation, the inventor acknowledged, that the major constructive problem of the machine is significant friction between the parts of the mechanism when must be done tens carry for two or more digital positions.

The machine of Gersten is not as elaborate and easy to operate, as the machines of the other early inventors, but nevertheless, it is well-designed and fully capable of calculations device. Interestingly, there is a letter
from Johann Müller from 9 February 1784 to his friend Lichtenberg in Göttingen, in which he writes the following about Gersten: “Unexpectedly, I found the calculating machine of the former local Prof. Gersten in the castle in Darmstadt, of which I hereby provide you with a description and drawing. Maybe you can make some use of it. It is strange that the thought of whether not appropriated in perfection is what I give you on my wooden models to be the more comfortable and faster installation of the given digits.”

Biography of Christian Ludwig Gersten

Johänn Christian Ludwig Gersten (or Gerstein) was born on 7 February 1701, in Gießen, a town in the German federal state of Hessen. He was the son of Johann Justus Gerst(en) (1666-1712), and Maria Margaretha Uhrban (1666-1741). Johann Gerst was a lawyer, Fürstlich-Schwarzburgischer Kanzler und Konsistorial-Präsident in Sondershausen (a town in Thuringia), who married Maria Uhrban in 1692, and they had seven children: Carola Henrica Eleonore (1693-1720), Johann Christian (b. 1695), Juliana Charlotte (1698-1726), Christian Ludwig (1701-1762), Friedrich Ludwig (1703-1705), Christine Frederike (b. 1706), and Johann Maria Lucia.

From 1718 Gersten studied law and mathematics at the University of Gießen and at the beginning of the 1730s he traveled to London, England, to improve his mathematical knowledge. In London, in 1733 he became a fellow of the English Royal Society. In May 1733, he returned back to Gießen, to accept the position of a professor of mathematics at the University of his hometown, which he held until 29 Apr 1745.

As a scientist, Gersten is primarily known for his dissertation work, published later as a book, describing a series of experiments, using the barometer, titled “Tentamina Systematis Novi ad Mutationes Barometri ex Natura elateris Aerei demonstrandas, cui adjecta sub finem Dissertatio Roris decidui errorem Antiquum et vulgarem per Observationes et Experimenta Nova excutiens” (see the nearby image). Gersten as a matter of fact was the first scientist to find out, based on observations, that dew did not fall from the heavens, but ascended from the earth, especially from plants. He is also the author of several other books in the fields of astronomy, physics, and mathematics.

As we already mentioned, in 1735 Gersten traveled again to London, to present to the Royal Society his project of an arithmetical machine.

It seems Gersten was quite an active person not only in the field of science but also in public affairs, which later led him into severe troubles. Gersten was admired in 1725 for his calculating machine by Landgrave of Hesse-Darmstadt Ludwig V, and by his son, Prince Georg II, who became Landgrave in 1726. In the early 1740s, Gersten was deposed from his office after refusing to submit to the sentence of a court of law, in a lawsuit with his brother-in-law Johann Friedrich Wahl (1693–1755), a Professor and from 1735 Rektor der Universität Gießen, and in 1744 he wrote a petition to the Landgrave Georg II, which was considered as offensive. The Landgrave accused Gersten and initiated a trial against him. Having a presentiment what will be the result, Gersten decided to escape justice and in July 1744 he left the town.

Initially, he settled in Altona bei Hamburg, and informed the University officials, that he was not going to return to Gießen and lost his position in April 1745. Then he departed to St. Peterburg, Russia, maybe to some other places also, but finally decided to return to Germany. And then his disrespect to the Landgrave and the attempt to escape from justice finally got him into big trouble. In September 1748 he was arrested in Frankfurt am Main by request from Darmstadt, and condemned to lifetime detention at the castle Marxburg bey Braubach (see the nearby image).

Gersten never recognized his mistakes and repeatedly addressed the court with offensive petitions. Interestingly, despite his problems with justice, in 1748 he was partly restored as a professor at the University of Gießen and was allowed during his stay in the castle to teach young people in mathematics. Gersten was eventually released as late as 1760.

Christian Ludwig Gersten died on 13 August 1762, in Frankfurt am Main.

In 1735 was published the first book of six volume set of Jean Gaffin Gallon—Machines et inventions approuvées par l’Academie Royale des Sciences, depuis son établissment jusqu’a présent; avec leur description, in which are described several calculating machines. In one of the books (Tome 4) was described the machine arithmetique of the French mathematician and inventor Hillerin de Boistissandeau, sent for approval to the Academie in 1730.

The machine of Hillerin is quite similar to the earlier Lépine’s machine (a solid, but simple adding device, with limited practical usefulness), so obviously Boistissandeau was strongly influenced by Lépine. Actually in the publication (see desciption of Hillerin’s machines) there are three separate articles, which described three different machines, but the second and the third are essentially improvements of the first one.

It seems at least one copy of the device was manufactured, preserved now in the collection of CNAM, Paris. The dimensions of the device are: height: 6.00 cm, width: 17.00 cm, length: 30.50 cm. The weight is 3.250 kg. Materials used are: wood, leather, iron, brass, and textile.

The machine of Boistissandeau has six digital positions, appropriate to the french monetary system in the 17th century. The rightmost position is for deniers, that’s why its wheel is divided into 12 parts, the next is for sols (the wheel is divided into 20 parts), remaining wheels are decimal (wheels are divided into 10 parts).

Entering and resetting the numbers is done by means of a stylus with two edges—short and long, which can be stuck into openings of the input wheels. When the short edge of the stylus is used, then will be rotated only the upper (input) disk and it can be set to 0. When the long edge of the stylus is stuck, then will be rotated not only the upper (input) disk, but also the lower disk of the calculating mechanism, and the number will be entered into it. The small wheels, which are placed over the big wheels are working as revolution counters and are used during a division operation. In these wheels is stored the quotient of the division, while below in the main mechanism is stored the remainder.

The five wheels (marked with w in the upper figure), which are placed between the six small wheels-revolution-counters, can be rotated by means of a special rod. These wheels are not connected to the calculating mechanism and are used as temporary storage for intermediate results.

Bellow, each input wheel is placed a small window, in which can be seen digits, inscribed on the wheel below. Here can be seen the result of the calculations. Over the digital wheel actually are inscribed two rows of digits. The first row is used during adding and multiplication, and the second—during subtraction and division. Which row of digits can be seen is determined by the rods (marked with B-B on the figure), which are moving a plate, covering one of the rows. Over the input wheels are placed small axles, which are stopping the styles during the rotation of the input wheels, and actually are determining which digit will be entered.

Below the digital disk, which digits can be seen in the windows below the input disk, are mounted on the same axes 3 disks. The first disk is a pinion-wheel, which can have 10, or 12 (according to the digital position of the wheel) teeth. This wheel takes the carry from the neighboring position (this is the reason that the rightmost position doesn’t have such a wheel). After this wheel is placed one-tooth wheel, which during each revolution will be engaged with the wheel of the higher position and will rotate it to 1/10 (or 1/12) revolution. The carrying is not direct but by means of an intermediate pinion-wheel, which is placed in the same plane, as the one-tooth wheel of the previous digital position and with pinion-wheel of the next digital position.

The lowest wheel actually is a ratch-wheel, and together with a rod and spring forms a system, destined for fixing the position of the digital positions mechanism.

The small wheels-revolution-counters also have openings, by means of which can be rotated, thus resetting the wheels. Bellow these wheels are placed ratch-wheels, which are fixed by means of rod and spring. The transfer of rotation from the main counter-wheels to these wheels is done by means of a special tooth on the big wheels, which once during a full revolution pulls a rod, which rotates to one tooth the ratch-wheel of the appropriate revolution-counter. Their digits are seen in the windows over each wheel.

The major fault of the first machine of Boistissandeau is its tens carry mechanism. The friction is huge and if it is necessary to propagate several consecutive carrying operations, then must be applied a vast effort and the mechanism can be blocked or even broken. That’s the reason in the second variant of the machine (see the nearby figure), Boistissandeau changed the tens carry mechanism.

Here the tens carry mechanism is made by partial pinion-wheels (actually a rod with an attached sector with several teeth on the edge). These rods are moved by means of a spring, which is connected to the mechanism of the junior position. This system already has the advantages of the tens carry mechanism of the Pascaline, and allows the carrying to be done without any effort. A similar mechanism is used for the wheels-revolution-counters. Another new element is the possibility to add mechanisms of new digital positions to the machine and to change the mechanisms of the digital positions, which allows the machine to be used for counting in the different numeral systems (monetary systems, weights, lengths, etc.)

Boistissandeau proposed also a third variant of his arithmetical machine (see the nearby figure), which again has improved the tens carry mechanism by lengthening the rod, which is stretching the spring, and decreasing the diameter of the pinion-wheel, which takes the carry, so it is required smaller effort during the carry.

Biography of Hillerin de Boistissandeau

The French mathematician and inventor Jean-Baptiste-Laurent de Hillerin, Seigneur de Boistissandeau and Seigneur de Jumaville, was born on 24 (baptized on 26) July 1704, in Paris, the first child in the noble family of Jean-Baptiste de Hillerin de Boistissandeau (13 Nov 1664-14 May 1732), conseiller au Parlement de Bretagne et du Roi, and Marie-Catherine Moreau de Villiers (born 7 Dec 1679). The family had also a daughter—Marie Catherine Armande (6 July 1709-23 Sep 1742).

The young Hillerin de Boistissandeau was energetic and passionate about the study of science. Abbé Robert, a former parish priest of Bourges, was his tutor. Growing up in the family Château du Boistissandeau (Castle of Boistissandeau) from the late 16th century (see the lower image), in the vicinity of the town Les Herbiers, western France, he made many developments around the castle and in particular construction of large raised orangeries with attics, granaries, and rooms to house servants. He was interested in physics and mathematics, and later in instrument making. Besides his calculating machine, de Boistissandeau was known as an inventor of various instruments, including a regulateur de parquet (a clock, used as a reference to other clocks, so that everyone is at the same time) in 1732, a surveyor and odometer in 1744, a portable barometer in 1758, etc.

Hillerin de Boistissandeau was a Counselor of the Parliament of Bretagne and was appointed adviser to the Board of Auditors of Paris by 1744. Chevalier Hillerin de Boistissandeau was also a Gentilhomme ordianire de la chambre du Roi and from 1744 membre correspondant de l’Académie Royale des Sciences (section of physics and mathematics) in Paris. He was a friend of the prominent french scientist René Antoine Ferchault de Réaumur, who made frequent visits to the Castle of Boistissandeau and even had a reserved room on the first floor of the castle, equipped as a small laboratory.

Hillerin de Boistissandeau married on 17 August 1735, in Paris, to Marie Agathe Bouret de Beuvron (24 Jan 1711-31 January 1794), daughter of Guillaume Bouret de Beuvron and Mathilde le Camus. The pair had eight children—six daughters and two sons (Marie Catherine (1736-1794), Antoinette Henriette (1737-1794), Louis François (1738-1799), Marie Agathe (1740-1794), Catherine (1742-1774), Julie (1744-1790), Louise Adélaïde (1750-1790), and Armande (1752-1820).

Seigneur de Boistissandeau died on 15 February 1779, in the Castle of Boistissandeau, happy to live not long enough to see the French Revolution. During the massacres of War in the Vendée, in 1793 his castle was looted and partly destroyed by the Republican army. Moreover, on 31 January 1794, a group of hussars-republicans raided the castle and killed his widow, the 83 years old paralyzed Marie Agathe, together with her daughters Antoinette Henriette and Marie Agathe.

When in 1724 the German mechanic Anton Braun (1686-1728) got an appointment as a mechanic and optician of the imperial court in Vienna, Austria, he started to design a calculating machine for the purposes of the court. Braun finished his work in 1727, producing a calculating machine of very good design and workmanship. When in the same year he presented the machine to the Holy Roman Emperor Karl VI, he was so impressed, that later appointed him as Imperial instrument maker, and granted him a diamond chain (with the portrait of the Emperor) and a huge sum of money—10000 guilders.

It seems at the same time when Braun designed and made the calculator, and presented it to the Emperor (we will call it the first machine of Braun), he devised a similar device, but with a different calculating mechanism (let’s call it the second machine of Braun). Obviously, Braun knew the machines of previous inventors, like Poleni (the first machine’s calculating mechanism is based on the pin-wheel of Leibniz and Poleni), and Leupold (the second machine’s calculating mechanism is based on the switching latch of Leupold, and the appearance of both machines is similar to Leupold’s device.)

There is an interesting story, connected with the first machine of Braun. One of the biographers of Poleni, the Frenchman Jean de Fouchy Pajil Grandjean, claims in his 1762 book “Eloge de Jean POLENI, Marquis du St. Empire, (né 1683 mort 1761)”, that …having heard that Mr. Brawn, a famous mechanic in Vienna, presented a similar machine to the Emperor, Poleni destroyed his machine and no more wanted to rebuild it. Despite the fact, that Fouchy was in strict contact with Poleni (when alive) and knew him personally, this story is quite questionable, not only because it is not compatible with the gentle character of Poleni. It is possible Braun to had gotten information about Poleni’s machine (Braun worked under the supervision of the imperial engineer Johann Jacob Marinoni, who was in correspondence with Poleni and perhaps visited him in Venice), and so decided to use the idea of Poleni in his construction, the history of inventions is full of cases like that. In fact, if Poleni didn’t manage for almost 20 years to manufacture and demonstrate a working copy of his machine, obviously he was not interested in this device at all and fully deserved to be outrun by others.

The first calculating machine of Anton Braun is quite big (almost 40 cm diameter and over 20 cm height) and a fancy device, finely decorated and looking like a Renaissance table clock cylinder, made of gold, steel, silver, and brass.

The example of the first machine, which survived to our time (see the upper image), has an engraved dedication (in Latin) to the Kaiser Karl VI and also the signature “Antonius Braun S.C.M. Opticus et mathematicus”, with the year of completion 1727. The whole inscription is: MACHINA ARITHMETICA PER QUAM ADDITIO, SUBSTRACTIO, MULTIPLICATIO ET DIVISIO ETIAM AB IGNARIS ARITHMETICES FACILLIME PERAGUNTUR. AUGUSTISSIMO ATQUE INVICTISSIMO ROMANORUM IMPERATORI CARLO SEXTO, GERMANIAE, HISPANIAE, HUNGARIAE, BOHEMIAE REGI, ARCHIDUCI AUSTRIAE MACHINAM HANC ARITHMETIC AMIN PERPETUAE GRATITUDINIS TESSERAM SUBJECTISSIME DICAT, DEDICAT CONSECRATQUE HUMILLIMUS INVENTOR ANTONIUS BRAUN S. C. M. OPTICUS ET MATHEMATICUS. 1727.

The example on the image is not the original one, made by Anton Braun in the 1720s, but a copy, made in 1766 by his son—Anton Braun the Younger (1708-1776), who just like his father was a skillful optician and watchmaker (the case was made by famous Munich sculptor Johann Baptist Straub).

The calculating mechanism was based on the pin-wheel (or the sprocket wheel), invented by Leibniz and Poleni. The machine’s six-place setting mechanism is in the form of six circular segments arranged in a circle on the top, with nine sliders each (for digits 1 to 9), which move the relevant pins radially outwards on the pin-wheels below. Turning the crank adds the entered number to the result mechanism (12-digits with complementary numbers shown), and the result is shown in the windows along the periphery of the cover (the silver-plated part). The setting mechanism can be rotated with respect to the result mechanism so that both multiplication and division are possible. The machine also featured a single-digit revolution counter.

The second calculating machine of Anton Braun (see the image below) is a much smaller device, similar in appearance to the first machine (round shape, crank in the middle, concentrically arranged numerical windows, and magnificent decorations), but its calculating mechanism is almost identical to the Leupold’s machine and it is based on a ratchet-wheel. This machine probably was only begun in the workshop of Braun, but after his early death in 1728, it was finished as late as 1736 by his son and by the famous French mechanic Phillippe Vayringe (1684-1746), who was hired by the Emperor to fix the machines, kept in his collection. The only surviving example of the machine (on its lid is engraved Braun invenit, Vayringae fecit) (Invented by Braun, manufactured by Vayringe) is now in the exposition of Deutsches Museum, Munich.

The second calculating machine of Braun is commonly named Leupold-Braun-Vayringe machine, due to the fact, that the idea of the calculating mechanism was proposed by Leupold, the construction was made by Braun, while the actual manufacturing was made by Vayringe. It is believed that Braun had already gotten to know and realized Leupold’s construction in detail before his volume Theatrum arithmetico-geometricum was published in 1727. Leupold himself reported that he had been dealing with calculating machines “for more than 20 years”, that he “had released four to five types” and that he “could show their workings to different friends”.

The machine featured a single central so-called adapting segment, which allowed the number of special, complicated parts to be greatly reduced. Below the setting mechanism is placed a set of vertical cylinders, each with nine rods of different lengths rising from its top. For example, if digit nine was entered, the shortest rod was rotated to the outside, and then one full turn of the crank turned the central adapting segment once around the central axle. It consisted of a disc with various steps as well as a segment with nine cogs. When it was turned once round, it passed the setting cylinders, on each of which a certain rod pushed the corresponding step outwards, whereupon the cog-segment of the adapting segment engaged a cog-wheel of the result mechanism and thus rotated the numbered disc to the correct digit in the corresponding window. Thus, the smaller the entered digit was, the later the adapting segment engaged, and fewer cogs were moved. Multiplication was done by repeated revolutions of the crank, as a place-shift mechanism enables multiplying with multi-digit multipliers. Subtraction (and division) were done using the 9-complements of digits.

Even though the tens-carry mechanism of the machine did not function properly in every place, the idea of a central adapting segment was a great innovation that found extensive use in several brilliant mechanical calculators some 200 years later on, like the magnificent Curta of Herzstark, even though it used a stepped drum as the central element.

The collection of Deutsches Museum, Munich (the world’s largest museum of science and technology), contains not only the original of Leupold-Braun-Vayringe machine but also a very beautiful modern replica with a transparent glass lid (see the nearby photo).

Biography of Anton Braun

Anton (spelled also Antoni and Antonius) Braun was born on 22 October 1686, in Möhringen an der Donau (bei Tuttlingen), a small town on the upper Danube, in Baden-Württemberg, Germany, in an old Bürger family, mentioned to live in Möhringen as long ago as in 1491. Anton was the first child from the second marriage of Hans Jacobus Braun (born 25 July 1651) and his wife Franziska Riestler (Hans Jacobus Braun had three daughters and two sons from his first marriage). Anton Braun had a younger brother, Johann Georg (b. 27 May 1688), who also became an optician and instrument maker, but could never reach the technical brilliance of his elder brother.

Hans Jacobus Braun used to work as a mechanic and watchmaker, so obviously, Anton learned the basics of mechanics in his parental home.

Anton Braun probably married young in his hometown, because in 1708 was born his son, Anton Braun Jr. (der Jüngere) (1708-23.10.1776), who also became a skillful instrument maker, optician, and watchmaker as his father, and made the copy of one of his calculating machines, still preserved in Technischen Museum, Wien.

At some point, Braun left his hometown to go to Vienna, most probably to study at the University of Vienna. There on 19 April 1712, Braun, designated as “University optician and mathematician” married in Cathedral St. Stephan, to Maria Magdalena Steinin (the daughter of Georg Stein, the postmaster at Ettlingen in Swabia, and his wife Maria Eva).

Braun probably left Vienna soon after his marriage, because he established mechanical workshops in Prague and Milan in the following years. During this period, Braun became one of the most prominent instrument makers of his time and was highly appreciated by the Imperial Engineer and professor at the University of Vienna—Johann Jakob Marinoni (see the nearby portrait). Braun was warmly recommended by Marinoni and worked for him in the years 1719-1722 as a surveyor in cadastral surveying in the duchy of Milan.

Anton Braun returned to Vienna in 1723, and the next year he was appointed to the prestigious position of Kammeropticus und Mathematicus at the Austrian court, due to his outstanding precision mechanical, and mathematical skills. Three years later, he sat down as a candidate for the post of Imperial instrument maker (Kaiserlicher Compaß- und Instrumentenmacher). And he won (there were four candidates), presenting to the Emperor his advanced calculating machine, which he constructed in 1724 and which was already in use at the imperial court.

Braun apparently got in favor of the Holy Roman Emperor Karl VI, because he was not only appointed as an imperial instrument maker but was also granted a 12-diamond chain (value of 500 guilders), occupied with the portrait of the Emperor (kept now in the Museum in Rathaus Möhringen) and a huge sum of money—10000 guilders. The 10000 Gulden were never paid out, however, because of war-related expenditures and financial difficulties of the Viennese Court under Empress Maria Theresia, the daughter of Karl VI. Nevertheless, Braun bequeathed half of his assets to his hometown, so 6000 guilders were used for charity and the construction of a hospital.

A circular sundial made by Anton Braun in 1719 is kept now in the collection of the Adler Planetarium in Chicago.

Unfortunately, Braun’s tireless zeal and restless activity used up his physical powers early, and he died too young (41 years old) from a long-running lung disease, on 20 April 1728, in Vienna. His brother Johann Georg also got the support of Marinoni and succeeded Anton’s position as Kaiserlicher Optikus.

In 1727, after the death of the German scientist and engineer Jacob Leupold was published the 8^th volume of his encyclopedia Theatrum Machinarium. This volume, entitled Theatrum arithmetico-geometricum is the best-illustrated work on calculation and measurement published during the 18^th century. It describes and illustrates the calculating devices and machines of Kircher (Schott), Grillet, Leibniz, and Poleni, along with Napier’s rods and several calculation tables (interestingly, Leupold missed the Pascaline, the most famous calculating machine of the time). It also discusses and illustrates the various analog devices available, including slide rules and sectors, and other calculating and measuring rules, as well as systems of computing using the fingers. In this volume, Leupold not only mentioned that “he was interested in calculating machines more than 20 years”, and “he had four or five types brought out”, and that “he had been able to show the effect to different friends”, but also described an original calculating machine, designed by himself.

Obviously an example of the above-mentioned calculating machine of Leupold has never been manufactured. In fact, Leupold defined himself as Mathematico und Mechanico (i.e. Mathematician and Mechanic, what we today would call Engineer) because he did not produce machines in his pursuits, but he studied them, corrected the errors he found in those designed by others, and designed machines and solutions of his own.

The Mechanical Calculator of Jacob Leupold

The calculating machine of Leupold has a circular shape which will very soon become very popular in the world of mechanical calculators. Yet in 1727 the calculating mechanism and the form of Leupold’s machine will be used by the German mechanic Anton Braun, who designed a similar device. Several machines, which appeared to be similar (not only) externally to Leupold’s will be devised later by Philipp Matthäus Hahn, Johann Helfrich Müller, Johann Reichold, and others.

The numbers are entered into the calculator by means of six small digital wheels, placed around the handle in the middle of the lid. Rotating this handle to a full revolution in a counterclockwise direction will transfer entered in the input mechanism number to the six dials (digital positions), placed in the outer ring (marked with A on the nearby figure), which present units, tens, hundreds, etc. The resulting mechanism has nine positions—the nine dials F, mounted on the outside ring (marked with C in the figure). The dials F have two graduations—the first is used during addition and multiplication, the second—during subtraction and division. The digits of the result are pointed by special pointer-arrows, which are rotating around the middle of the axes.

On the same axes, but inside of the machine (see the figure below), are placed 10-teeth stop-wheels G, M, I…, which can be rotated only in one direction (clockwise), and can be fixed by means of the small rod D and spring-rod C.

The motion from the input (six small dials) to the result (nine bigger wheels in ring C) is transferred by means of the 9-teeth sector-teeth-strip N, which can be rotated around axis w. On the strip N, on the plane, perpendicular to it is attached a thin plate X, which is illustrated separately in the upper right part of the figure. The left side-ward surface of the plate is straight, the right is formed as nine steps of the same height. The function of this plate is to raise the teeth strip, which will engage with the result mechanism and will rotate it. That is done in this way:
Below each one of the entering wheels is placed a ring with a spiral inclined upper surface A, which is shown in the upper left part of the figure. Each position of the input mechanism has an eccentric rod (marked with m, n, and o), which has a bulge in its upper part, contacting the plate X, and another bulge in its lower part, contacting to the spiral surface of the ring. Rotating one of the six entering wheels, thus rotating the appropriate ring, we actually will raise or take down these eccentrics in a plane, perpendicular to the plane of the teeth-strip and parallel to the plane of the plate X in this way, that upper bulge will raise and fix in the upper position this plate for a different distance, and in this way, a different number of teeth will be engaged with the top-wheels G, M, I. Thus, the number of the teeth, to which will be rotated on each of these wheels, is determined by the length of the engaging way of the eccentric with the plate X.

The invented by Leupold mechanism became quite popular at the end of the XIX century in several calculating machines, e.g. machines of Dietzschold, Büttner, and Pallweber. It will be called Schaltklinke in German, in English it will be called switching latch, intermittent contact, adjustable pawl, and selectable ratchet.

In the middle of the machine is placed an auxiliary counter, which scale can be seen around the handle. This counter is destined to count the revolutions of the handle.

The tens carry mechanism (see the nearby figure) is made as follows:
On the same axes, on which are fixed the stop-wheels G, M, I…, are fixed also 10-teeth wheels O, P, Q… Between them are placed intermediate wheels K, L, M… Each intermediate wheel has an attached finger, fixed with a spring (d, e, g, j…), and in odd-numbered wheels, this finger is placed over the wheel of units, while in even-numbered wheels this finger is placed below it. In one revolution of the units-wheel Q the finger de will rotate to 1/10 revolution the wheel of the tens P, and thus the tens carry will be performed. The tens carry from the other wheels will be performed in much the same manner.

The Calculating Drum of Jacob Leupold

In the Theatrum arithmetico-geometricum of Leupold is described also a calculating tool, the so-called Rechenscheiben (calculating drum), based on Napier’s rods (see the lower figure). Let’s examine its construction.

The Rechenscheiben (calculating drum) of Leupold (in the nearby image you can see a later replica of die Rechenscheiben, from the exposition of Arithmeum Museum, Bonn) consists of 11 ten-sided disks, mounted on common axes (marked with F in the drawing). The cylindrical housing is broken through so that only two levels of the number series (two sides of the disks) are visible.

The right side disk is fixed, while the remaining ten disks can be rotated with a hand. On the surface of the device are placed 10 round openings (marked with d), which are used for fixing the angular position of the disks, by means of pins (c), pushed in the appropriate opening, as it is shown on the right side of the figure. On the surface of each of the 10 sides of the rotating disk are inscribed the digits of the same Napier’s rod, while on the side of the fixed disk, with face to the operator, is inscribed a column of digits from 1 to 9. The multiplicand is entered by rotating the proper disks and fixing them by means of the pins against the fixed column of digits (multiplicands) of the fixed disk.

Leupold also mentioned another variant of the device. The modification consists of replacing the disks with rings the width of a number strip. The rings are pushed onto a wooden cylinder and can be adjusted independently of each other.

Biography of Jacob Leupold

Jacob Leupold was born on 22 July 1674, in Planitz, a village near Zwickau (then in Electorate of Saxony), to George Leupold (1647-1707), a skilled mechanic (cabinet-maker, turner, sculptor, and watchmaker) from Johanngeorgenstadt (Erzgebirge), and Magdalena Leupold.

Since early childhood Jacob scrutinized his father’s work, developing an interest in various mechanical things and as he described it later, …I had not only the opportunity of seeing how different things have been made, but also manual work made me strong. Due to his “ailing physical condition,” it did not seem advisable to let the young Leupold learn a trade, so George Leupold sent him to Zwickau’s Latin school. In 1693 Leupold started to study theology at the University of Jena, but he did not give up his interest in mechanical things—he also attended lectures of the well-known astronomer and mathematician Erhard Weigel. In 1694 Jacob left Jena, since he obviously could not afford the registration fee, and switched to the University of Wittenberg, but soon left it for the same reason—lack of money.

Finally, in 1696 Jacob was enrolled for free at the University of Leipzig, where he apprenticed to an instrument maker, and in 1698 he started to produce globes, quadrants, sundials, and measuring and drawing instruments. He was so successful that he broke off his studies to set up a mechanical workshop. He was helping to design and build many instruments needed for experimental physics studies and his interests had fully changed from theology to mechanics and mathematics.

In 1701 Leupold got a position as a hospital warden in George Military Hospital, thus obtaining not only regular income but also enough free time to dedicate himself to mechanics. In the same 1701, he married Anna Elisabeth, and they had three sons and three daughters, who all died young except for one daughter. Unfortunately, Anna Elisabeth also died young in March 1713.

In 1704 Leupold became ill from an unknown illness, possibly a stroke, which affected his memory and hearing. In his discussions on the capacity of humans for labor, he notes that he was able to lift and move far more weight before his illness.

In 1714 Leupold resigned from the hospital and managed his instrument shop with several assistants. The shop produced both musical and scientific instruments. During this time, he was associated with the University of Leipzig as a mechanic.

In 1715 Leupold was appointed a member of the Berlin Academy of Sciences. This position quickly attracted two other plum appointments: Commissioner of Mines to Saxony and Counselor of Commerce to Prussia.

Leupold is also credited as an early inventor of air pumps. He designed his first pump in 1705, and in 1707 he published the book Antlia pneumatica illustrata. In 1711 following the advice of its president Wilhelm Leibniz, the Prussian Academy of Sciences acquired Leupold’s pump.

In 1720 Leupold started to work on the manuscript of his famous encyclopedia Theatrium machinarum, a nine-volume series on machine design and technology, published between 1724 and 1739. It was the first systematic analysis of mechanical engineering in the world. Leupold’s intended audience was not highly educated elites, but rather the common mechanic, that’s why the book is written in German, not in Latin (the dominant language of science and the universal means of communication in Western Europe up to the end of the 17^th century). His work is addressed …not to the learned and experienced mathematicians who are already, or should be, better acquainted with them… [and most of whom] have studied mechanics more as a subject of curiosity and a hobby, than with any view of service to the public. The people we had in mind were rather the mechanic, handicraftsman, and the like, who, without education or knowledge of foreign languages have no access to many sources of information…

In the 1720s Leupold rejected several offers by the Russian tsar Peter the Great to move to St. Petersburg.

At the beginning of January 1727, when the eighth volume of the Theatrum Machinarum was nearing completion, Leupold fell gravely ill and died on 12 January 1727, at the age of only 52.