Category: Timeline Stories

In early 1850s a certain Ernest-Narcisse Lobbé, a Parisian horloger-mécanicien (watchmaker and mechanic), created one of the first keyboard calculating machines in the world (after the machines of James White, Luigi Torchi, Jean-Baptiste Schwilgué, and Dubois Parmelee). The machine (so-called Additionneur mécanique à touches) was patented in 1855 (French patent №24582 from 04 Nov 1855, see the lower patent drawing).

This single column (only one-digit numbers may be entered) key-driven adding machine seems to be a sound and very well-designed device, but it remained only on paper and nothing is known about the device and the inventor—Ernest-Narcisse Lobbé.

The improved arithmometer of the Reverend Thomas Hill (1818-1891), a Unitarian clergyman in Waltham, Massachusetts (later he became a famous scientist, educator, President of Harvard University, and one of the most profound yet brilliant mathematicians in the USA), was the first key-driven calculating machine, made in the United States, which was preserved to our time (see US patent №18692 of Hill from 24 November 1857).

The calculator of Hill was not the first machine of this type neither in the world, nor in USA. His compatriot Parmelee patented a key-driven adding machine seven years before, in 1850, but it remained only on paper. The same is true for the machine of Orlando Lane Castle, which (interestingly) was patented on the same day—24 November 1857. We don’t know if the two inventors knew each other, but anyway, the construction of their machines is quite different.

Several key-driven calculating machines had been already built in Europe a long time before (e.g. machines of James White, Luigi Torchi, Jean-Baptiste Schwilgué, Victor Schilt, and Ernest-Narcisse Lobbé). We can hardly suppose that Hill knew something about the machines of European inventors, but he probably knew the machine of Parmelee, and decided to make his own and better device (it was not a hard task, because the machine of Parmelee was rather primitive).

In 1857 Hill applied for a patent for “a new and useful Mechanical Calculator for the Purpose of Performing Various Mathematical Calculations” and sent a wooden model to the US patent office. It is known, that up to 1880, the Patent Office required inventors to submit a model with their patent application. Inventors placed great importance on their models and viewed a well-executed model as the key element in obtaining a patent. Sadly, in 1877 there was a disastrous fire in the US Patent Office building and many models were destroyed. Fortunately, the model of Hill survived and was preserved to our time.

The device has overall measurements of 12.5 cm x 7.5 cm x 30.8 cm, and was made of wood, metal, and paper.

The patent shows two numeral wheels, each having seven sets each of large and small figures running from 1 to 9, and the cipher marked on their periphery. The large sets of figures are arranged for addition or positive calculation, and the small figures are arranged in the reverse for subtraction or negative calculation. The wheels are provided with means for the carry of the tens, very similar to that found in the Pascal machine. Each of the two wheels shown is provided with ratchet teeth which correspond in number with the number of figures on the wheel.

Spring-pressed, hook-shaped ratchet pawls (marked b in the figure), are arranged to be in constant engagement with the numeral wheels. These pawls are each pivotally mounted on the end of the levers (marked E), which are pivoted at the front end of the casing.

The levers E, are held in normal or upward position by springs f, at the front of the machine. Above each of these levers E, are a series of keys which protrude through the casing with their lower ends resting on the levers. There are but six keys shown in the drawing, but the specification claims that a complete set of nine keys may be supplied for each lever.

The arrangement and spacing of the keys are such that the greater the value of the key the nearer it is to the fulcrum or pivot of the lever E. The length of the key stem under the head or button of each key is gauged to allow depression of the key, the lever E and pawl b, far enough to cause the numeral wheel to rotate as many numeral places as the value marking on the key.

A back-stop pawl for the numeral wheels, (marked p), is mounted on a cross-rod at the top of the machine. But one of these pawls is shown, the shaft and the pawl for the higher wheel being broken away to show the device for transferring the tens to the higher wheel.

The transfer device for the carry of the tens is a lever arrangement constructed from a tube F, mounted on the cross-rod m, with arms G and H. Pivoted to the arm G, is a ratchet pawl i, and attached to the pawl is a spring that serves to hold the pawl in engagement with the ratchet of the higher-order numeral wheel, and at the same time, through its attachment with the pawl, holds the lever arms G and H retracted as shown in the drawing.

As the lower-order numeral wheel passes any one of its points from 9 to 0, one of the teeth or cam lugs n, on the wheel will move the arm H, of the transfer lever forward, causing the pawl i, to move the higher-order wheel one step to register the accumulation of the tens.

The functions of the Hill mechanism would, perhaps, be practical if it were not for the physical law that “bodies set in motion tend to remain in motion”. Just like his forerunner Parmelee, Hill made no provision for overcoming the lightning-speed momentum that could be given the numeral wheels in his machine through manipulation of the keys, either from direct key-action or indirectly through the carry of the tens. Imagine the sudden whirl his numeral wheel would receive on a quick depression of a key and then consider that he provided no means for stopping these wheels; it is obvious that a correct result could not be obtained by the use of such a mechanism.

Considerable unearned publicity has been given to the Hill invention on account of the patent office model having been placed on exhibit in the National Museum at Washington (at the present time the model is kept in the collection of the Smithsonian Institution in Washington).

Other key-driven machines were presented in the following years, in particular by the Americans Leonard Nutz (in 1858) and Joseph Alexander (in 1864), Austrian Friedrich Arzberger (1866), Gilbert Chapin from New York (1870), and David Carroll from Pennsylvania (1876) among others. Improvements in these machines led to the first practical key-driven machine—the famous Comptometer by Dorr E. Felt, presented in 1885.

Biography of Thomas Hill

Thomas Hill (Jr.) was born to Thomas Hill (1771-1828) and his second wife, Henrietta (Barker) Hill (1774-1824) on 7 June 1818, in New Brunswick, New Jersey, a centrally located town between New York and Philadelphia along an early thoroughfare known as the King’s Highway and situated along the Raritan River, an important hub for Colonial travelers and traders.

Thomas Hill the father (see the lower image) was in his youth a farmer near Tamworth in Warwickshire, England . He was a Unitarian, and in 1791, during the prevailing political, religious, and social upheaval in England, emigrated to the United States in search of religious liberty. In his new country, he began as a farmer, then started a business as a tanner in New Brunswick, served for many years as a judge of the local court of common pleas, and married his second wife, Henrietta Barker, whose father likewise had been driven from England during the religious persecutions following the Birmingham riot.

A lover of nature, Hill the father taught his children (Thomas had three brothers and five sisters, and he was the youngest) the scientific names of plants and encouraged an interest in the natural sciences. Unfortunately, Thomas lost his parents yearly, as Henrietta Hill died on 28 June 1824 and Thomas Hill (Sr.) died on 2 April 1828, thus Thomas became an orphan by the time he was only nine years old.

Thomas had little formal schooling in his early years, but his mother and sisters taught him to read and cipher. A keen observer with a retentive memory, he was a constant and wide reader and developed an early interest in botany, science, philosophy, and mathematics. By the time he was twelve years old, Thomas had read the works of Benjamin Franklin and Erasmus Darwin. After three years of formal schooling, to make a little money, Hill served as an apprentice in the newspaper Fredonian from 1830 to 1833. Then until October 1834, he studied under his eldest brother at Lower Dublin Academy in Holmesburg, Pennsylvania, then at Leicester Academy in Massachusetts, leaving in 1837. Although he was interested in civil engineering, but since no place offered itself, Hill became an apprentice to an apothecary in his home place, serving in this capacity until 1838.

By May 1838 Hill managed to convince his brothers, who supported him, for his bent for the ministry, and started to prepare for Harvard College, where he entered at the end of 1839 and earned a Bachelor of Arts degree in 1843. At Harvard, Hill distinguished himself in mathematics and invented an instrument for calculating eclipses and occultations, for which he was awarded the Scott Medal from the Franklin Institute. He also published a little book of poems entitled Christmas and Poems on Slavery, dedicated to Eliza Lee Follen, who was active in the anti-slavery movement. In 1845, Hill received his Doctor of Divinity from the Harvard Divinity School and entered the ministry for 14 years.

Hill served at the First Church of Waltham, Massachusetts from 1845 to 1859. It was during this time that Hill established his reputation, not only as a man of God, but also as a scientist, educator, and writer. In the next few years, Hill published First Lessons in Geometry (1855), two mathematical textbooks, Geometry and Faith (1849), a book describing the essence of Hill’s religious doctrine, and several papers on mathematics and astronomy for the American Association for the Advancement of Science. In 1857, he wrote an article about astronomy for the new Appleton’s Encyclopedia. A popular speaker, Hill gave the Phi Beta Kappa oration at Harvard University in 1858 and presented a series of Lowell Institute lectures on the Mutual Relation of the Sciences in 1859.

Soon after his graduation in the summer of 1845, on 27 November of the same year, Thomas Hill married in Waltham, Massachusetts, to Anne Foster Bellows (1817-1864), of Walpole, New Hampshire. The couple had six children—Mary Bellows (1846-1911), Henry Barker (1849-1903), Katherine (1851-1926), Elizabeth Joy (1854), Anne Bellows (1857), and Thomas Roby (1864-1923) (the nearby image pictures Thomas Hill with his son Henry and his grandson Edward Burlingame. Henry Barker Hill became a known American chemist and director of the Chemistry Laboratory at Harvard University. Edward Burlingame Hill (1872-1960) became a good American composer.)

In 1857 Hill obtained a patent for a key-driven calculating machine, second in the USA. During his final years in Waltham, Hill served on the Waltham School Committee and was constantly encouraging and promoting new ideas and methods of instruction, including the introduction of phonetic spelling in public schools.

In 1859, Hill accepted, much against his wishes, the presidency of Antioch College in Yellow Springs, Ohio. His appointment was ill-timed, however, as the American Civil War forced the college to close in 1862. That same year Cornelius Conway Felton, the President of Harvard University, died suddenly, and Hill was asked to succeed him.

Returning to Harvard University, Hill had high hopes for the future and brought about a number of changes. Under his administration, the undergraduate curriculum adopted an elective system, permitting student choice in selecting courses. The standards for admission were raised, an Academic Council made up of the faculties of the college and professional schools was established, scholarships for the support of graduate students were endowed, a program of University Lecturers was introduced, and new chairs for professorships in geology and mining were founded.

Despite these apparent successes, Hill’s years at Harvard were not happy. He had difficulty in his dealings with faculty and in governing the University. In addition, his first wife, Ann, died in 1864 while he was in office. Two years later, on 23 July 1866, Hill married Lucy Elizabeth Shepard (28 Sep 1837–9 Feb 1869) of Dorchester, his former student from Antioch College, and they had one son, Otis Shepard Hill (28 Dec 1868–3 Mar 1946), but unfortunately, Lucy Elizabeth suffered from an incurable illness and died at the beginning of 1869. Hill’s experience with his own physical problems at this time also contributed to his unhappiness (he claimed to have injured his testicle while gardening, an incident that made him wary of laboratory instruction at Harvard, warning students not to exert themselves too much in their studies.) Tired and overwhelmed both personally and professionally, Hill resigned his office on 30 Sep 1868, weighed down by “personal bereavements”.

After the death of his wife Lucy in 1869, Hill spent a year resting and traveling. In 1871 he was elected to the Massachusetts state legislature from Waltham and served for one year. In 1872, Hill sailed with his friend Louis Agassiz on an expedition to South America. Returning to the ministry in 1873, Hill accepted a position at the First Church in Portland, Maine. For the next eighteen years, Hill was happy spending his time preaching, writing, lecturing, and pursuing scientific and educational experiments.

In the spring of 1891, Thomas Hill became ill, suffered for several months, and died on 21 November in Waltham, Massachusetts, and was buried at the local Mount Feake Cemetery. His house (see the lower photo), is still reserved and is listed on the National Register of Historic Places.

On 24 November 1857, Orlando Lane Castle (1822-1892), a professor of Latin, Oratory, Rhetoric, and Belles-Lettres at the Shurtleff College in Alton, Illinois, received a patent for a calculating machine, called Improved arithmometer for adding (see US pat. №18675) of very interesting design, operated by a clock spring, wound manually. The next year (1858) Castle reissued his patent (USRE 551) and patented another calculating machine, which was essentially an improved version of the first one (see US pat. №21941).

The calculating machine of Castle seems to be the second in the USA keyboard adder, after the machine of Dubois Parmelee (or third, since the machine of his compatriot Thomas Hill was patented on the same day), and sixth in the world, after the machines of White, Torchi, Schwilgué, and Lobbé.

The first calculating machine of Castle was a key-driven adding machine (see the nearby patent drawing). It was the first machine with a nine-key scheme, connectable to the different orders.

The mode of operation of the machine is as follows:
1. Before commencing, the register should be set free of the driving wheel D by turning back the crank J, and the register-wheels turned till every wheel presents its 0 opposite the openings in the plate H, and then the register frame should be brought forward again, with the secondary driving-wheel m, belonging to the first or unit-register wheel k’, in gear with the driving wheel D, and should be secured in this position by bringing the crank J into the first notch in the bar K, counting from the right hand on Fig. 3.

2. The unit-column is then added by depressing the keys S’, S2, etc., one after the other in the same numerical order as the figures in the column of units to be added, and at every depression of a key the unit register wheel k’ is caused to make 1, 2, or more tenths of a revolution—that is to say, as many as the number indicated on the key depressed—and every time the revolution of the unit-registering wheel is completed and the 0 is brought opposite the opening in the plate H the tooth n of the wheel o that is attached to its secondary driving-wheel gives one-tenth of a revolution the tens-registering wheel k2; and if the sum of the column of units is sufficient to complete a revolution of the tens-wheel, the secondary driving-wheel, gearing with the wheel n that is attached to the tens-wheel receiving motion from the said wheel n, will bring the tooth r on the second wheel o into operation on the hundreds-wheel k3.

3. When the units-column has been added in the above manner, the crank J is raised out of the notch in the bar K of the register, and the register thus thrown out of gear with the driving-wheel F, and, without disturbing the register-wheels, the whole of the register frame is moved far enough to allow the crank J to enter the second notch of the bar K, which brings that secondary driving wheel m which gears with the tens-registering wheel k2 opposite the driving-wheel D, and on the crank J being thrown forward into the notch that secondary driving-wheel is brought into gear with D. The addition of the column of tens can then proceed with the same manner as the column of units.
4. The above-mentioned process should be followed for adding of columns of hundreds, thousands, etc.

The second machine, called by the inventor Improved Arithmometer for Addition (pat. №21941 from 2 Nov. 1858) is a smaller and improved version of the first one (see the nearby patent drawing).

It is not known if the calculating machines of Castle have been manufactured or influenced somehow the development of other calculating machines.

Biography of Orlando Lane Castle

Orlando Lane Castle (1822-1892) was born in Jericho, Chittenden County, Vermont, on 20 July 1822, the third child (of eight, four sons and four daughters) to Augustus Castle and Almira Bostwick Lane-Castle (1795-1864). Their eight children were: Sarah Celestia (1819-1864), Emily Bostwick (1820–1888), Orlando Lane (1822-1892), William Augustus (1824-1910), Alonzo (1827-1828), Eunice Aurelia (1829-1905), Adoniram Judson (1832-1852), and Mary Ellen (1837-1892).

Augustus Castle (see the nearby image), born on 9 July 1791 in Essex, Vt., son of Abel Castle and Sara Woodworth Aubery, married Almira Lane at Jericho on 31 Oct. 2816. He was an industrious farmer in Jericho, Vermont. Augustus’ farm joined that of his elder brother, Joel (1790-1858), but in March 1831, he removed with his family from Jericho to Alexandria, in the wilderness of Licking County, central Ohio, where his younger brother Sanford (1793-1840) had removed in 1817 and where Augustus will eventually buy a farm. Augustus Castle died on 22 March 1880, in Granville, Ohio.

Orlando’s early intellectual opportunities were quite limited. His early life was stamped with that energy and strict economy which were indispensable to success on the part of those who extorted the means of subsistence from the earth by farming. At the age of eighteen, the turning point of his life was reached, he was determined to be a teacher, and he entered Granville College (now Denison University), Ohio. In 1846 Orlando graduated from College, securing the honor of his class. During his college course, he was almost entirely thrown upon his own resources for the means to meet his expenses. In the winter he taught school, and during the last three years in college, he taught lower classes.

After graduating, Castle spent one more year as a tutor at Granville College, and later, for several years he had charge of the public schools of Zanesville, Ohio, where he exhibited great efficiency and secured a high reputation as an instructor. In 1853, Castle accepted the chair of Latin, Rhetoric, Oratory, and Belles-Lettres in Shurtleff College, at Upper Alton, remaining there for almost 39 years, closing his class work on Tuesday, 29 Jan. 1892, just a day before his death.

Professor Castle received the degree LLD (Doctor of Laws) from Denison University in 1877. He was a meta-physician, a mathematician, and a logician, an excellent teacher. Dr. Castle was a holder of quite a few patents not only for calculating machines but also for farming machinery—a grain-harvester, a grain-binder, a nut-lock, etc.

Orlando Lane Castle married Olive Loveland Thrall (b. in Granville, Ohio, on 14 November 1830—died in 1911) on 15 August 1848, and they had three children—Elizabeth (b. 13 October 1849—died 8 February 1851), Lucius Marsh (b. 16 January 1852—died 1932), Linus Thrall (b. 12 December 1853).

Orlando Lane Castle died of pneumonia on Saturday morning, 30 January 1892, in his house at 1831 Seminary Street in Upper Alton, Illinois (still preserved, see the nearby image).

The calculating machine of the Swiss clock-maker and precision-mechanic Viktor (or Victor) Schilt (1822-1880) was exhibited in 1851 at the Great exposition of the works of industry of all nations in Crystal Palace, London, and received an honorable mention and a bronze medal, placed after the calculating machines of Izrael Staffel and Thomas de Colmar.

The machine of Victor Schilt was a single column (only one-digit numbers may be entered) key-driven adder, almost an exact copy of the first calculating machine of Jean-Baptiste Schwilgué and there is an obvious reason for this resemblance—Schilt worked about two years in the workshop of Schwilgué in Strasbourg (around 1847-1848), before to return to his hometown (Grenchen, canton of Solothurn, Switzerland), where he later built many tower clocks.

In the workshop of Schwilgué in Strasbourg Schilt was mainly busy working on tower clocks, but undoubtedly he was engaged also in the making of calculating machines, because soon after leaving Strasbourg in 1848 he made the first example of his machine. At the 1851 London Exhibition Schilt reportedly received an order for the manufacturing of 100 machines (which seems an enormous amount for the time), but refused to produce them, probably because he wasn’t the inventor.

Now a copy of the Schilt’s machine, a solid and well-manufactured device, featuring the inscription V. Schilt, Mechaniker in Solothurn, is in the collection of the Smithsonian Institution in Washington (see the nearby photos).

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

It is a wood and metal device with measurements: 11.9 cm x 26 cm x 14.5 cm.

The front, top, and mechanism of the machine are steel, while the case is wooden. The plate and zeroing knobs on the top and the nine-digit keys across the front are made of brass. The machine adds numbers up to 299. Only one-digit numbers can be entered. The result is visible in a window on the plate.

In 1841 in Paris the young French student Timoléon-Louis Maurel (1819-1879) (later a good French clock-maker and inventor) devised and in the next 1842 obtained a patent for 15 years (see patent No. FR14529 from 18 November 1842) for his first calculating machine for multiplication and division, which certainly can be used for addition and subtraction also.

Several years later (in 1846) Maurel patented (this time together with his fellow student and friend—Jean Jayet (1820-1904), an improved version of the machine (see patent No. FR4777), and in 1847 they got a Great Britain patent (No. 184711928). Interestingly, Maurel and Jayet later claimed that they were unaware of the existence of Pascal’s machine when they embarked on the design of their own, while they were still students in philosophy class. Moreover, they didn’t mention the machine of Thomas also, and later there was an industrial property dispute between Thomas and Maurel (this dispute was not in the legal field since the first patent Thomas has long since expired), although they obviously “borrowed” the stepped drum mechanism from Arithmometer of Thomas.

The prototype of the device was presented at the Exposition Nationale de 1849 in Paris and caused a sensation, being awarded the gold medal by the President of the Republic, Prince Louis-Napoleon Bonaparte. An article in the l’Illustration magazine reports that the 10-digit machine costs 2000 F and recommends the government to order twenty examples, to be distributed among the main ministries. Subsequently, the machine was awarded the Prix de mécanique of the Fondation Montyon (1000 F, enough to finance the construction of a new prototype).

Maurel was a holder of another 15-year French patent from 1860 for a calculating machine (No. 46757), again with a stepped cylinder mechanism, but with simpler construction, as well as several patents in other countries, e.g. Austria and England.

This remarkable for its time calculating machine became famous under the name Arithmaurel.

In 1849 the famous French physicist and author, Father François-Napoléon-Marie Moigno (1804–1884), published an article for Thomas, Maurel, and Jayet (La Presse, 6 March 1849, reprinted in Cosmos, Jan. 1854, see the article of Moigno), whom he affectionately describes as “young artists”. His article evokes their common effort: After ten years of difficult studies, incessant combinations, expensive trials, incredible privations, and frightening misery, they built the first machine. Proud of this first success, they left Isère for long journeys from their village to Paris, from Paris to Lille, and from Lille to London, asking everywhere for financial support (fifteen thousand francs). They finally meet a patron who gave them the money for paying patent rights, offered them enough to live on and pay the wages of the workers they employed, and send them “to one of those humble villages of Franche-Comté, where to build with so much perfection and at such a low price the innumerable cogs of their watches and clocks”.

Encouraged by the early success of the machine, the inventors planned to start mass production of their device, and established the company “T. Maurel, J. Jayet & Cie.”, registered at the beginning of 1851 in the court of Grenoble. In 1848 the inventors settled in Paris, trying to organize the production of the machine. Around 1850 they assigned the production of the device to the famous Austrian-French clockmaker Joseph-Thaddäus Winnerl (1799-1886), one of the best watchmakers in Europe. Winnerl, was born in Mureck, Styria, and was trained and worked in Austria, Germany, and Denmark, but in 1829 he settled in France, where in 1831 he established his own workshop in Paris (43 avenue de l’Observatoire), and soon became an outstanding manufacturer of chronometers, marine clocks, and balance wheels. Interestingly, Maurel and Jayet even lived some time at the same address as the workshop and obviously were engaged in the production.

Until 1854, Winnerl was not able to build any of the 8-digit machines (a minimum for any professional usage) that had been ordered, but until the late 1850s about thirty handmade copies of Arithmaurel were produced in his workshop, and several devices managed to survive to our time. Unfortunately, the construction of the machine was too complex for the technology of the middle of the 19th century. The devices had a very clever design but were expensive, fragile, and error-prone, so they were not competitive with the simpler, but cheap and reliable calculating machines of Thomas de Colmar.

The dimensions of the machine are: 20,5 x 18,2 x 29 cm. Materials used are: bronze, enamel plates, and mahogany (for the case).

The calculating mechanism is based on the stepped drum of Leibniz. The multiplicand is entered by means of the stems in the upper part of the machine. Pulling or pushing these stems, the stepped drums in the box will be moved, so different numbers of teeth will be contacted by the calculating mechanism during the rotation of the handle. The multiplier is entered by means of the four keys in the lower part of the machine and can be seen in the four dials near the keys. On the dials are inscribed two rows of digits (from 0 to 9) on the left and right parts of the dial. The first half is used during division, while the other—is during multiplication. After entering the multiplicand and multiplier, by rotating the handle on the right side of the box, the calculating mechanism and drums will make one revolution and the result can be seen in the central dials. The upper row of dials is for storing the intermediate result during the multiplication of more than two numbers.

During the division, the keys must be rotated in the direction, contrariwise to the multiplication. The reset mechanism is placed on the side.

Let’s see the operating instructions for the machine:
1. Always reset the machine before starting a new operation.
2. To add 668 to 258, enter 668 on the sliders, then scroll through a division with the handle of the dial of the units. 668 is displayed in the totalizer. Enter 258 on the sliders and run one more division on the handle of the unit dial. The final result, 926, is displayed on the totalizer. There is no need to reset the unit dial between the two operations.
3. To subtract 258 from 364, enter 364 on the sliders, then scroll through a division with the handle of the dial of the units. 364 is displayed in the totalizer. Then enter 258 on the sliders and run through a division in the reverse direction with the handle of the dial of the units. The final result, 106, is displayed on the totalizer.
4. To multiply 668 by 258, enter 668 on the sliders, then scroll through 8 divisions with the handle of the units dial, 5344 is displayed in the result windows, and the units dial displays 8. Then cycle through 5 divisions the handle of the tens dial, 38744 is displayed, and then 2 divisions to that of the hundreds. The final result, 172344, is written on the totalizer. The dials display 00258.
5. The division is a sequence of subtractions that require a lot of concentration from the operator.

The described in the patent machine can be used for the multiplication of 8-digit to 4-digit numbers, the result mechanism is also 8-digit. There are also machines with different numbers of positions.

According to the above-mentioned article of Father Moigno from 1849, using the Arithmaurel a multiplication of two 8-digit numbers can be done for 18 seconds, while a division of 15-digit to 8-digit numbers can be done for 24 seconds, which was a remarkable calculating speed at that time.

The end of Arithmaurel was miserable. After numerous problems with production, on 8 April 1856 (one year before the basic patent expires), the company T. Maurel, J. Jayet & Cie. was dissolved. Maurel was responsible for liquidating it, completing the Arithmaurels being manufactured to sell them, and finding a buyer for the patents. Some unfinished machines, as well as lots of parts, will be kept for a long time and finally went for scrap in 1914.

Biographical data about Maurel and Jayet

Little is known about the inventors of this amazing for that time machine, the engineers Timoléon-Louis Maurel and Jean Jayet. They came from the same part of the country—southeastern France. Maurel originate from Gap, the capital and largest town of the Hautes-Alpes department, while Jayet was from Voiron, a French municipality in Isère department.

Timoléon-Zoé-Louis Maurel was born on 16 November 1819 in Barâtié (now Baratier). He was the son of Antoine Maurel from Embrun, a lawyer at the court of Gap, and Anne Thérèse Joubert. We know that he was a student (as well as Jayet) in Paris in 1842 when he applied for his first patent. Maurel had a son Leon Mary Louis (1857-1902). He married on 15 Dec 1873 in Paris to Virginie Bourgeat (1826-1877), born in Corenc, daughter of Laurent Antoine Bourgeat and Katherine Lawrence. Maurel died in 1879 in Paris.

Jean Pierre Honoré Jayet Dauphiné (known as Jean Jayet) was born on 15 May 1820 in Voiron. He was the eldest son of Jean Baptiste Jayet (Dauphiné) (b. 1792–d. 7 Aug 1852), a Voiron baker and innkeeper, and his wife Anne Guillaud (1795-1864). Besides Jean Pierre, the family had two younger sons—Antoine Victor (b. 1821), and Gaspard Jules (b. 1824), and three daughters—Anne (b. 1819), Emilie Adèle (b. 1827), and Eleonore Sophie (b. 1829). Jean Pierre married two times: On 7 October 1858 he married Adrienne Suzanne Vieux in Noyarey, Isère, Rhône-Alpes; then on 18 February 1860, in Voiron, he married Seraphie Marie Josephine Borel (born 1832), and they had a daughter, Lucie Josephine (born 1861). Jean Jayet died in Paris on 27 June 1904.

It seems around 1850 Maurel and Jayet both have been appointed assistant weights and measures checkers (vérificateur poids et mesures), respectively for the 10th and 11th districts of Paris and for the district of St. Denis. Jayet worked for many years in that job (as an auditor), while Maurel soon left to seek a more profitable and interesting position. In his 1860 patent, Maurel was specified as a “mechanics engineer”.

Timoléon Maurel was a holder of a total of ten patents in various fields, including pharmacy, but especially watchmaking (e.g. for pendulum, mechanical leech machine, etc.) After the failure of the production of Arithmaurel, he resettled on rue du Parc-Royal in Paris and quickly reoriented his activity in a workshop manufacturing travel alarm clocks, which he patented and which respond better than the Arithmaurel to the solvent demands of the nascent industrial nation.

After the slide adders of Claude Perrault, César Caze, and Heinrich Kummer, in 1889 the French teacher, school director, inventor, scientist, and writer Louis-Joseph Troncet (1850-1920), created his version of this type of calculator, which he called Arithmographe. Troncet’s invention became so popular that the term “Troncet-type” is often used to refer to this class of devices. The device was in production for almost 30 years. Millions of units of this type were sold. It was on the market until the 1970s!

Louis-Joseph Troncet was a holder of four French patents for calculating devices: Brevet №123135 from 21.03.1878, №133106 (22.10.1879), №171473 (3.10.1885), and №197579 (18.04.1889) (never published as fees were not paid). The first patent (from 1878) was for a slide adder with dials, called Numerateur, which has never been put in production (see the lower patent drawing of the device).

The devices of Troncet are typical of the small, usually hand-held, stylus-driven adding machines. They are often known as crook or cane adders, because of the shape of the input slots. The operator moved a stylus up or down the slot n spaces to add or subtract the digit n. If there was not enough space to move n places, the stylus was forced to go over the hook and effect a carry to the next digit.

The next three patents are for different versions of the Arithmographe (see the patent drawing of the third version from 1889).

Namely, the third version of the Arithmographe (see the lower photo) featured so clever and reliable construction, that became a market hit at the end of the 19^th and the beginning of the 20^th century. The first devices were produced by Librairie Larousse and were sold normally in a small notebook with a set of multiplication tables.

The Arithmographe was made of paper and copper alloy (copper, brass, bronze), its dimensions are 10 x 13,6 x 0,5 cm; the weight was 300 g. A good description of the workings of the device can be seen in the manual (see the lower image) from a very popular in the US analog of the Arithmographe, the Baby Calculator. There is also a detailed description of Arithmographe in the book Фон-Бооль, Приборы и машины для механическаго производства арифметических действий. Описание и оценка счетных приборов и машин, see description of Аритмографъ Тронсе.

The Arithmographe of Troncet used flat metal bands with notched edges to represent digits. These bands were moved with the stylus to enter numbers. The instrument has seven crook-shaped columns that reveal the edges of eight notched bands. The crook at the top of each groove is designed to ease carrying or borrowing.

Eight holes below the columns labeled ADDITION, show the results of the addition operation. Eight holes above the columns labeled SOUSTRACTION, show the results of the subtraction operation. There is no zeroing mechanism.

Louis Troncet manufactured and sold another calculating device, a dial adder, called Totalisateur (see the lower photo), which was a circular adding device (The Scottish pastor Brown’s Rotula Arithmetica from the 1690s can be seen as the archetype of all of these concentric toothed disk-adding devices). It however didn’t become a market hit, in contrast with the Arithmographe.

Biography of Louis-Joseph Troncet

Louis-Joseph Troncet was born on 16 November 1850, in Montierchaume, a village near Chatearoux, in the Indre department of central France. He was the son of Joseph Troncet, cultivateur-cantonnier (farmer and cantonier), and his wife Marie Robrolle-Troncet, а housekeeper. In 1859, Marie Troncet gave а birth to a boy, Henri, who died five days later. The next day died Marie, so Louis lost his mother only nine years old.

As a boy, Troncet was a brilliant student and obtained a Brevet Supérieur, then a certificate d’Aptitude Pédagogique at the Normal School in Chatearoux, and then was appointed as a school director in the village of Buzançais (30 km NW of Chatearoux). His career continued as a teacher and school director in Reuilly (50 km NE of Chatearoux), then in Saint-Florentine (near Vatan) from 1900 to 1912, then from 1912 until his retirement in Selles sur Nanon, a village close to Buzançais.

In addition to his job as a teacher, Troncet did mathematical, scientific, and educational research that led him to many inventions (besides his calculating instruments), as follows:
– HOROMETER—a dial displaying the local time in different countries of the world (in 1904)
– CHRONOGRAPHE—an instrument, which for a given date establishes concordance with the different calendars existing in the world
– COSMOSPHERE—an instrument, which indicates after orientation the relative positions of the stars according to the place where we are on Earth (in 1914)
– ROSE MAGNETIQUE—a compass rose that turns exactly, that is to say, all the points of which turn themselves towards the points of the horizon which it represents (in 1915)

Troncet also published numerous books and booklets in various topics, mainly in the area of domestic animals and diseases (some co-written with other authors), including textbooks for intuitive reading which have been translated into several languages. Let’s mention only: Calculateur mécanique instantané. Arithmographe Troncet. Larousse, 1890; Horomètre, cadran donnant l’heure universelle. G. Gambart, 1904; La Basse-cour. La poule, le dindon, la pintade, le pigeon, le canard, l’oie, le cygne, le paon, le faisan, le lapin, le léporide, le cobaye. Races, alimentation, hygiène, accidents et maladies…; Arboriculture pratique. Larousse, 1895; Le Jardin potager. Larousse, 1895; Premier livre encyclopédique: cours de lectures intuitives. Larousse; Le bétail: le cheval, l’âne, le mulet, le bardot, le boeuf, le mouton, la chèvre, le porc, le chien, le chat… Larousse, 1902; Le bétail. Larousse, 1895; Les Animaux de France utiles ou nuisibles. Larousse, 1901.

Troncet was a titular member of the Société Astronomique de France (from 1910), and lecturer at l’Institut Géographique de Paris. At the end of the 1890s, Troncet left his post as a school director in Reuilly, to collaborate in Paris in the writing of the great Larousse dictionary and of the universal Larousse magazine, and became editor-in-chief of the magazine Après l’Ecole founded in 1885 by René Leblanc.

Troncet was a holder of many awards. In 1899 the Ministry of Education promoted him to Officer of the Academy and Officer of Public Instruction. At the Universal Exhibition of 1900, Troncet received from the International Jury the diploma and silver medal of the Press of Education. In 1903 he was awarded a medal for his scientific inventions from Fabricants et Inventeurs Français. He was a holder of a medal of the House LAROUSSE.

On 14 November 1876, Louis-Joseph Troncet married in Buzançais to Anna Arthémise Berthouly (see the nearby portrait). The family had three boys: Louis Joseph Marie (born 9 August 1877), Félix Maurice Antony (born 23 May 1879), and Georges François Fernand (born 31 January 1884). Antony Troncet (1879-1939) became a known French painter, illustrator, engraver, and poet. Joseph Troncet became the Head of the Department at the Paris City Hall. Fernand became a schoolteacher like his father but unfortunately died young.

Louis-Joseph Troncet died on 15 February 1920, in his family home on rue de l’Indre in Chateauroux. His wife Anna Arthémise will follow him in 1930.

Several people experimented with versions of simple mechanical calculators, that included strips of metal with numbers marked on them mounted in a frame, where a stylus was used to slide these strips up and down. Let’s mention only Claude Perrault, who invented the first form of this class of devices around 1670, and César Caze, who created his version at the beginning of the 1700s. One problem with Caze’s machine was that it wasn’t possible to perform carries from one column to another. This issue was solved in 1846 by a German musician and amateur mechanic, working in St. Peterburg, Russia—Heinrich Kummer, then by Billiard in Paris (Brevet d’invention N° 6703 from 1847), and others.

In the first review of Kummer’s adding device was mentioned, that the main idea the inventor borrowed from Slominski’s adding device (in his first presentation Kummer mentioned the adders of Roth and Slonimski), which had already been presented to the Russian Academy of Sciences in St. Peterburg previous year, 1845. In fact, the internal mechanism of the device of Kummer, which went down in the history of computing facilities as Kummer’s Calculator (Счислитель Куммера), is totally different, moreover, it appeared to be considerably more cheap and effective, than the adding device of Slonimski.

On 4 September 1846, Kummer presented to the Russian Academy of Sciences his slide adder. The reviewer on his device was the famous mathematician Mihail Ostrogradsky. In his review, he noticed, that the main idea was borrowed from Slonimski, but the construction resulted was incomparably simpler and more convenient in use. One of the major advantages of Kummer’s adding machine compared with Slonimski’s device was portability. Ostrogradsky noted that to a sheet of paper folded eight times, would be as thick as this device, but the length and the width will be much more. With smaller sizes, it would be inconvenient to deal with it.

In 1847 the device was presented as Kummer’s Selbstrechner in the newspaper St. Peterburgische Zeitung, Dienstag, 20 Mai (1. Juni) 1847.

One of the early devices, kept now in the collection of CNAM, Paris (see the lower image), is a large “desktop” version with dimensions 40 x 8,5 x 10,8 cm, and a weight of 95 g, but there are much smaller “pocket” devices with dimensions: 10 x 6 x 0.3 cm). There are also devices with multiplication and division facilities (writing pad). Materials used are cardboard, paper, and ferrous alloy. The device calculates in rubles and kopecks.

The slide adder of Kummer is probably the first slide adder equipped with a shepherd’s crook-carrying mechanism, which makes it particularly interesting.

The numbers are entered by means of stylus and laths, which can be moved along the troughs. At the side of the laths, the numbers from 0 to 9 are marked. The carrying is done by means of teeth. Each lath has a tooth, which can touch the similar tooth on the adjacent lath and move it in one position upwards or downwards if it is necessary.

The upper part of the device is for сложение (addition), lower part is for вычитание (subtraction). In the bottom left-hand corner, one can read деление (division) and in the bottom right-hand corner, умножение (multiplication). On the ivory lower part one can write auxiliary information needed in multiplication and division. A small round hole in a slide means that you have to draw the stylus to the right end and a large square hole that one has to make a tens carry by drawing the stylus in the direction of the crooked end.

To reset the device all laths must be slid downward to the stop position, thus in all result windows will appear zeroes.

The adding device of Kummer is the first device of this type, manufactured in quantity. Kummer received on 29 March 1847, a free 10 years patent (an extremely rare advantage) for his device (Привилегия на счетный снаряд, выданная учителю музыки Куммеру, 29 марта 1847 года, на 10 лет). The first seller (and probably manufacturer) of the adder was the famous watchmaker Иоганн Генрих Мозер (Johann Heinrich Moser (1805-1874) had a workshop and several watchmaker shops in Russia), later (since around 1870) the device was produced by the company Mechaniker und Optiker I. E. Milk (Мильк) in Moscow in significant quantity and later on was serially released (with various modifications) up to the 70s of the 20th century.

Kummer’s adding device was patented not only in Russia but also in France and USA. The French patent was filed in November 1847, by François Jacques Marc Auguste Billiard (1788-1858), an employee of the Ministry of the Interior (аt the time French patents could not be granted to foreigners, sо it can be assumed that Billiard was Kummer’s French agent). The USA patent 90275 of Kummer for Calculator (Improvement in computing-tablet) (see the lower image) was granted in 1869 to one Henry Kummer of New York, obviously the Americanized version of Heinrich Kummer of Dresden 🙂

Later on, adders like Kummer’s, for example, the Arithmographe of Troncet, became very popular and were manufactured in millions until the advent of the electronic pocket calculator in the 1970s.

There is a detailed description of Kummer’s Calculator (Счислитель Куммера) in the book Фон-Бооль, Приборы и машины для механическаго производства арифметических действий. Описание и оценка счетных приборов и машин, see the description of Kummer’s calculator.

Biography of Heinrich Kummer

The information for Heinrich Kummer in Russian sources is very scanty. It is mentioned only, that he was a teacher of music in St. Peterburg. Who was this mysterious person?

Carl Heinrich Gotthelf Kummer (known as Heinrich Kummer), was a German musician (bassoon player and pianist) and amateur engineer, born on 8 May 1809, in Dresden. He was the only son of the German bassoon virtuoso Gotthelf Heinrich August Kummer.

The father, Gotthelf Kummer was born on 23 January 1774, in Neustadt, near Dresden, as the third son of Johann Gottfried Kummer (1730-1812), the founder of the famous German musical family Kummers (Gotthelf’s elder brothers Carl Gottfried Salomon (1766-1850), and Friedrich August (1770-1849), also became famous musicians). Gotthelf was trained the music by his father and practiced chiefly on the bassoon, touring with great success in many European countries. Gotthelf Kummer died in Dresden on 28 January, 1857.

Following the steps of his father, Heinrich Kummer became a bassoon player and pianist but never managed to approach his father’s success. Instead of that, he demonstrated outstanding capabilities in the rather distant from the music field—mechanics.

As a boy, Heinrich learned to play several musical instruments, taught not only by his father, but also by several other famous German musicians, like Carl Krägen (1797-1879), Ignaz Moscheles (1794-1870), and Johann Hummel (1778-1837). Heinrich concerted with great success with his father all over Germany from being six years old, playing the piano and later bassoon. For example, in 1816, after a series of concerts, last in Munich, King Maximilian I Joseph of Bavaria awarded them with 300 golden ducats.

From 1827 to 1832 Heinrich was engaged as a bassoonist in the Dresden musical chapel, but in 1832, trying unsuccessfully to obtain a good permanent position as a musician, he left for two years for Poland, (a Russian province at this time), to work as a piano teacher in the family of the former administrator of the Lowicz principality, Obersten von Philippeus. In 1834 Heinrich went to St. Petersburg, Russia, where in 1837 he joined the Imperial Russian theater and opera orchestra as the first bassoonist.

While in St. Petersburg, Kummer designed not only his famous adding device, but also a bridge over Neva (in 1837), allowing traffic over the bridge while ships could simultaneously pass under it. The project was never realized, but the plan was preserved in Petersburg city archives. Studying for years birds and insects, Kummer constructed several automatic devices, powered by watch springs, which imitated the movement of fish in water and flying bird.

In 1847, after serving for ten years, Kummer received a full pension, and the next year he left Russia and settled in Schaffhausen, Switzerland. In 1851 he moved back to his home city, Dresden, where he continued to work as a music teacher.

Back in Switzerland and Germany, Heinrich Kummer was evidently more interested in shooting and rifles than in calculating devices. He made his rifles himself and even constructed a new System Kummer rifle (see the nearby image), which received prizes at several exhibitions in Frankfurt, Bremen, and Vienna. Moreover, he published a bestseller book about shooting (Der praktische Büchsenschütze, (The Practical Gunner), published in 1862, reprinted in 2013), and wrote many articles in the “German Rifle and Military Newspaper”, in which he dealt with the weapon and shooting-related questions. He also campaigned to introduce free-hand shooting in Saxony and helped set up two shooting ranges (Fischhaus near Dresden and Steiger near Pottschappel).

At the end of the 1860s, Kummer most likely visited the USA, as in 1869 in New York he received a patent for his calculating device (he used the English variant “Henry Kummer” of his name).

Heinrich Kummer died on 20 March 1880, in Dresden.

The Polish economist, financier, linguist, engineer and inventor Jan Józef Baranowski was the author of many technical inventions, 17 of which have been patented in France. Interestingly, at least five of them are for calculating devices:
1. Machine for obtaining the products of numbers without multiplying (Brevet №4587 from 1846 for Machine propre à obtenir les produits des nombres sans faire la multiplication).
2. Calculating watch operating the four rules of arithmetic (Brevet №2663 from 1847 for Montre à calcul opérant les quatre règles de l’arithmétique).
3. Tax-machine from 1848 (taxe-machine pour obtenir les résultats des calculs les plus compliqués même ceux des changes et arbitrages de banque, avec un contrôle instantané).
4. Machine for calculation of the votes in the elections from 1848.
5. Cylinder for wages and freight.
The first calculating machine was patented in the USA also (US patent №5746 from 1848 for reckoning machine).

1. Machine for obtaining the products of numbers without multiplying (Machine propre à obtenir les produits des nombres sans faire la multiplication).

Let’s examine the first reckoning machine of Baranowski, using the US patent (see the nearby drawing).
The first reckoning machine of Baranowski consists of a commercial table or ready-reckoner containing the various results previously calculated and arranged consecutively in units, tens, hundreds, etc. (as well as in fractional parts, when desired) of suitable apparatus for bringing the numbers of such table into view, of a face-plate with openings formed in it to admit of any portion of such commercial table or ready-reckoner being seen when required, and, lastly, of a number of accurately-fitted slides, any number of which can be withdrawn for the purpose of exhibiting the numbers constituting the required result, the other numbers not required for the result to be ascertained being concealed from view.

The slides and the face-plate are so adapted and arranged that the operator may readily see from the front of the machine which slides to withdraw in order to disclose any required result. The operation of the machine, then, consists in the display of the particular result required on the withdrawal of the proper slide by the operator when such result is to be exhibited by a single number or sum on the tabulated surface; but when the result is to be exhibited by or consists of two or more numbers, then two or more proper slides have to be withdrawn, by which the two or more numbers are displayed, which being added together give the final result, and the same principle is to be followed to any extent required, the machine being, of course, adapted to the particular kind of tabulated surface to be used with it.

Thus the ascertainment of the result by means of the machine becomes reduced to the simple operation of exhibiting to view the number constituting the result required or the numbers to be added together for such result with the greatest facility.

2. Calculating watch operating the four rules of arithmetic (Montre à calcul opérant les quatre règles de l’arithmétique).
The second calculating machine of Baranowski (see the lower patent drawing) was a simple adder, similar to the earlier machine of Lépine.

3. Tax machine (taxe-machine pour obtenir les résultats des calculs les plus compliqués même ceux des changes et arbitrages de banque, avec un contrôle instantané).

The Baranowski Tax Machine (see the nearby photo) was a specialized tabular calculator, built in France circa 1849, which was used for general employee payrolls. The machine was awarded a medal in 1849 at the French National Exhibition in Paris, attracting much curiosity through its method of controlling every type of account. Baranowski made a special machine for the Minister of Public Works to “control” the tariffs of all the French Railways. The machine has been exploited widely in France and England for calculating wages. One hundred machines were supplied to the various gold, copper, and malachite mines of Prince Demidoff. They have also been used for calculating interest at different rates (3, 4, 5, 6%). One was specially built in 1849 with calculations in Russian money for the office of the Emperor of Russia.

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4. Machine for calculation of the votes in the elections.
The machine for calculation of the votes in the elections of Baranowski (see the lower patent drawing) was designed in 1849. Actually Baranowski designed three different voting machines, the simplest being a box, containing a simple counting mechanism, where the voting boot had to be equipped with one box per candidate and the voter had to turn the crack at the counter of his favorite candidate. His second machine allowed for binary decisions, while the third machine was designed for choosing between more than two alternatives.

5. Cylinder for wages and freight.

The Baranowski Cylinder for Wages and Freight (picture of the Baranowski device from the catalogue of the Great Exhibition of 1851) was a specialized tabular calculator with 470 cells. It was exposed on the Great Exhibition of 1851. The construction and operation of the device is similar to the earlier Baranowski tax-machine.

Biography of Jan Józef Baranowski

Jan Józef Baranowski (AKA Jean-Joseph Baranowski (French), Ян Юзеф Барановский (Russian), John Joseph Baranowski (English)) was born on 7th September 1805, in Śmiłowiczach (now Смілавічы, Беларус), near Minsk, to the Polish nobleman and captain in the cavalry Marcin Baranowski (from Grzymała clan) and his wife Maryanna z Szalkiewiczów.

Jan Józef had shown, since infancy, a great predilection and capacity in mechanics. He was educated in a noble boarding school in Śmiłowiczach, then at the Public School and Classical Gymnasium in Minsk. There he particularly distinguished himself in the classes for physics and mathematics, and studied also with great eagerness the French and German languages.

In 1821 Jan Józef enrolled at Vilnius University, studying physics and medicine, but in 1825 he was transferred to the faculty of law, obtaining in this field a degree of bachelor in 1828.

Immediately after graduating in 1828, Baranowski was admitted into the office of the National Bank of Poland in Warsaw, and was promoted shortly to the post of Under-Secretary for foreign correspondence. In 1830-1831 Baranowski took part voluntarily in the November Uprising, participating in many battles. At the end of the uprising, he retreated to Austria where he was interned.

Since 1832 Baranowski was in exile in France. Initially, he settled in Gray, Lyon and Chalon-sur-Saône, where he worked as a banker and trader in department stores. In 1837 he moved to Paris, taking a job as a teller in the bank Jelski, Dussard et Compagnie. In the years 1843-1848 he worked as an inspector of the rail-road Paris-Rouen-Le Havre. For the purposes of the company he developed a bookkeeping system, that was highly appreciated and implemented by other French railway companies.
In 1848 Baranowski quit his job and devoted himself entirely to inventive activities. In the next years, he patented 17 inventions, between them: gas meter, ticketing machine, printing machine for tickets, automatic railway signaling (semaphore), several calculating devices (tax machine, voting machine, and two calculating machines). In 1851 he obtained, at the Universal Exhibition in London, a prize medal with a diploma for a small machine which printed in many colors, and stamped in the most accurate manner possible, railway, theatrical, and other tickets.

In 1871, after the Franco-Prussian War, France was ordered to pay a huge tribute. Baranowski presented to the authorities a plan for the government loan, which was approved with small modifications. For his proposal however he did not receive any awards, and embittered Baranowski decided to leave France and in 1872 he moved to London, where he took a job as an Under-Secretary to the Literary Association of the Friends of Poland, in charge of the development of dictionaries (Baranowski was a polyglot, who knew besides his native Polish, also German, French, and English.) In London, he published several books required in the study of languages, e.g.: Vade-Mecum de la Langue Francaise, The Student’s Anglo-Polish Grammar.

Jan Józef Baranowski died in London on 30 March 1888.

The Polish Jew Chaim Zelig Slonimski (1810-1904), a Hebrew publisher, astronomer, inventor, and science author, commenced his activities with calculating machines around 1838, when he, visiting Byelostok, heard that a Jew had spent there several days, collecting subscriptions for tables of calculations, which he had invented. The tables had no success, but Chaim decided to try to produce something better, and having once taken the idea into his head, it was soon accomplished. He returned home and designed a machine to perform addition and subtraction, but he had not the means to complete his instrument.

In the late 1830s Chaim Zelig Slonimski settled permanently in Warsaw as a guest in the home of Abraham Jakub Stern, the popular mathematician and inventor of various machines (including calculating). This occurred for the young author and scholar who had recently been divorced, thanks to Stern, who wanted him as a son-in-law for his youngest daughter, Sara Gitel. The match was finalized at the beginning of 1842, one month before Stern’s death. There is no doubt, that Slonimski was heavily influenced by his mentor and father-in-law Stern, but besides this valuable legacy, Slonimski must have been a very smart man, judging by the rest of his life.

Three calculating machines were invented and produced by Slonimski before 1843, one for addition and subtraction, one logarithmic device, and one for multiplication. The first account of his calculating devices is from September 1839, when he wrote to a friend, that he had built a calculating machine and that he was working on a 20-digit logarithmic device.

It seems Slonimski demonstrated firstly the adding machine, because in the June 1840 issue of the Vilnius newspaper Kuryer Litewski was announced (at that time Slonimski was in Vilnius to publish his mathematical handbook):
A Jew Slonimski born in Bialystok, recently invented a small machine for calculating, which thanks to its dimensions (length 10 inches, width 3 inches and 1 inch height), comfort, and low price deserves to be widely used. Everybody who knows digits only can, with the help of this machine, make calculations easily, fast, and without need to think. This machine can be seen at the inventor’s residence, where he is now working on a new machine for calculating logarithms. With the help of this machine one can simply and comfortably find the differences of Bruget logarithms, as well as natural logarithms up to 14 decimal digits.

The adding machine was presented also in 1841 in Königsberg, where Slonimski was invited through the recommendation of Bessel, the great astronomer, who taught at the university. Slonimski got permission to expose for inspection, in the university building, his calculating machine and had the pleasure to see it highly approved by the whole faculty. Slonimski obviously described (or demonstrated) his logarithmic device also, because there is a letter from Carl Gustav Jacobi to his brother, asking for support for Slonimski to demonstrate it in St. Petersburg.

The multiplication machine was based on a newly discovered theorem from number theory, called the Slonimski Theorem. The operation of the multiplication machine, which is more important, has been described by Slonimski himself in Russian. In principle, it was an implementation of multiplication tables, which resulted from the application of the theorem. Since the amount of related numbers was not that large, they were put on the cylinders, which—when moved appropriately—were showing the multiplication results in small windows.

Slonimski’s machines got high recognition during his lifetime. In August 1844, he brought his machines to Berlin, where he demonstrated them first to some prominent scientist as Alexander von Humboldt, Friedrich Bessel, Johann Encke, and others, then to the Royal Prussian Academy of Sciences, and his work was highly appreciated. The accurate results of his machines gained him here the same approbation, and although he did not communicate the theoretical principles on which the whole rests, yet, Humboldt recommended him to Friedrich Wilhelm IV, King of Prussia, where he saw, at his representation, his machines highly approved. Humboldt even intended to provide him with material means so that he could settle in Berlin and then occupy the chair of mathematics in one of the Prussian universities, but family circumstances prevented Slonimski from taking advantage of this offer.

In the same 1844, Slonimski published an article on calculating machines in the Journal für die reine und angewandte Mathematik, vol. 26, 1844, pp. 184–190 (see article of Slonimski). In 1845 an article “Selig Slonimski and His Calculating Instrument” was published in Illustrierte Zeitung, Leipzig, vol. 5, no. 110, 1845, pp. 90–92 (see article of Slonimski).

Next year, in April of 1845, he presented the multiplication machine to the Academy of Sciences in St. Petersburg, and obtained its recommendation for the Demidov Prize of the Second Grade (The Second Grade prize amounted to 2500 Rubles. For comparison, one should say that a university scholarship of 20 Roubles per 1 month could easily cover a student’s living and educational expenditures.), which was awarded to him on 24 June 1845. Moreover, the President of the Academy, Министр Граф Серге́й Ува́ров, presented the inventor before the Emperor, and a few days afterward the following Ukase (decree) appeared:
Ukase to the Senate.
The Hebrew, Selig Slonimski, born in the city of Bialystok, is hereby, in approval of the high merits which his learned and useful labours in the Mathematical branch have gained, raised to the rank of an Honorary Citizen.
Nicolas I.
Peterhof, 26 July, 1845.

In 1847 Slonimski applied for a patent in the USA (see the petition of Slonimski), stating that there was a company in New York— Neustadt and Barnett (of two Jews from Warsaw named Samuel J. Neustadt and David Barnett), who were interested in financing his invention and they apparently paid $300—at that time a very large sum of money—in order to get a patent. For unknown reasons, this application was unsuccessful. Barnett managed however to obtain a Great Britain patent on Slonimski’s behalf for the adding device and the third model of his multiplying device (British patent number 11441 of 1847). By a stroke of luck, Slonimski managed to sell the rights of the manufacture of his adding machine to England for £400. He invested the money in the acquisition of a fruit orchard in the town of Tomashov.

The theorem of Slonimski is derived from the Farey numbers (a sequence of the irreducible irrational numbers a/b where b<=n, which belongs to the segment /0, 1/ and is arranged in increasing order). Using this theorem, Slonimski composed a table with 280 columns, each of which contained 9 numbers. The table was engraved on the cylinders; as the main component of the device, these cylinders can both revolve around the axis (the shaft) and move (reciprocate) along it. Aside from the main cylinders, there are also 2 small cylinders with digits from 0 to 9 on one of them and the letters a, b, c, d, together with digits 1 to 7 on the other. The cylinders are driven with the use of handles, and fastened to the shaft end. While the small cylinders are immobile, the main cylinders are moved along their axis with toothed gearing, driven with screws, and mounted on the cover. There are also handles on the cover, which set the numbers (multiplicands).

The whole instrument is made of a flat wooden box, similar to a chessboard, 40 cm long, 33 cm wide, and 5 cm high. On the cover of the machine, there are 11 rows of windows. The first (lower) window shows the multiplicand. When the number is set in the first row, both letters and numbers appear in the windows of the second and third rows. Their combination is the code, which informs the operator which screw should be turned (and which cylinder is to be shifted). After this, windows 4-11 show the resulting numbers. The 4th row shows the product of multiplication by 2, the 5th by 3, the 6th by 4, etc. Finally, the products of all ranks are displayed. After adding them to paper, the desired product is obtained. Apparently, the convenience of this method was rather questionable, and it is no wonder, that there is no evidence of its systematic practical use.

More importantly, this machine was the only available device for discrete calculating. The basic principle of its work was the theory of numbers, rather than complicated mechanism alone. It was the mathematical art of the device, which was so highly appreciated by the Academy, and personally by the famous mathematician Ostrogradsky. As the Academy report noted, “the discovery of the basic feature of multiple numbers was the principle but not the only condition for composing this calculating machine… The inventor also should arrange the aforementioned 280 types in proper order and also invent a phantom key (the code). Finally, the surface of each of the six cylinders is covered with a complicated system of 2280 numbers and 600 letters with indicators. This artificial ordering demonstrates the shrewdness of its author’s mind, which raises Mr. Slonimski’s device to the level of an analytical mathematical instrument. It is not just a calculator, of which the main idea is represented by the numbers of its pinions.”
The Academy commissioned Slonimski to publish the proof of his theorem, together with a detailed description of the machine in the Russian language. The task was performed within a short time, and the book appeared in 1845.

Later on, other inventors made similar devices—August Leopold Crelle, Henry Knight, Herschell Filipowski. In 1881, a Russian Jew—the mathematician Zebi Hirsch Joffe, created a popular counting tool (a set, consisting of 70 rectangular bars with totally of 280 columns on all sides), named Joffe’s Counting Bars, based on Slonimski’s theorem.

For his calculating machine for addition and subtraction, the so-called arithmetical machine (see the patent drawing below), Slonimski also obtained a patent (Привилегия Слонимскаго) on 24 November 1845, for the period of ten years (see the patent of Slonimski RU1845-11).

A working example of Slonimski’s adding machine, made by the Warsaw mechanic and optician Jakob Pik, survived to the present and is kept in the collection of Museum of the Jagiellonian University, Poland (see below the photos of the device).

The adding device consists of two rectangular brass plates, in which there are curved incisions showing wheel dials. It has seven 24-teeth wheels, which can be rotated by means of a stylus, each corresponding to one decimal position. Windows above the incisions allow the display of results. On one side, the machine is used for additions (top plate), and on the other side, it is used for subtractions (back plate).

On the circumference are drilled 24 holes, appearing across the digits, and permitting the operator to advance the wheels from 1 to 9 units with the use of the stylus. A ribbon spring above each wheel, composed of a band, stops the uncontrolled advancement of the wheel. The teeth located between the wheels partially overlap, an important detail for the transmission of a carry. They are alternately placed above or below each other depending on the side that is used.

Slonimski’s design has a significant flaw—tens carry needed to be manually transmitted for each position, and if the operator was not careful, mistakes could be made.

Despite its flaws, it seems Slonimski’s adding device had a significant impact on the development of calculating devices, because only a year later, after Slonimski received a patent in St. Petersburg for his adding device, Heinrich Kummer designed in the same St. Petersburg a slide adder or what it’s now called a Kummer or Troncet type adder. Slide adders of this type became the most popular adding devices, and were manufactured for more than a century until the mid-1970s.

It seems after selling the rights to his calculating devices in 1847, Slonimski was no longer developing them, and transferred his efforts to other inventions.

Biography of Chaim Zelig Slonimski

Chaim Zelig Slonimski (also known by many name variations through Hebrew, Yiddish, Polish, and the funny Russian version Зиновий Яковлевич Слонимский) was born in a poor orthodox Jewish family on 31 March 1810, in Byelostok (Byelostok or Bialystok was one of the many towns in Russian Empire (now in Poland), that had a significant (almost 70%) Jewish population), in the Grodno Governorate of the Russian Empire.

He was the oldest son of Rabbi Avraham Ya’akov Bishka (1785–c. 1860), who belonged to a family of rabbis, who were writers, publishers, and printers, and his wife Leah (Neches) Bishka, daughter of Rabbi Yehiel Neches, an owner of a well-known House of Study (house of prayer) in Byelostok.

Avraham Bishka, also known as Bishke, ”Yankeleh” and “The Slonimer”, was a son of Rabbi Binyamin Bishka Hakohen Katz, a publisher, and printer. Avraham also was a scholar and teacher, but made his living as a pedlar of glassware, and made barely enough by it to support his numerous family. It is believed that Avraham worked (or was born) in Slonim (Слоним, another town in Russian Empire (now in Belarus), that had a significant Jewish population), and “The Slonimer” description became adapted by his descendants as “Slonimski”.

Besides the oldest son—Chaim Zelig, Avraham and Leah Bishka had a daughter, Zimke, and two younger sons, Avraham Avrom (who became a textile manufacturer and merchant), and Jonha (who had a glass shop).

Chaim’s family provided him with a good Talmudic education (he studied at the House of Study of his grandfather Yehiel Neches), and at an early age, he already looked upon as a smart boy and demonstrated an interest in mathematics.

There is an interesting (although lacking documentary corroboration) family story, told by Nicolas Slonimsky, a grandchild of Chaim Zelig Slonimski, concerning a solar eclipse that occurred near Bialystok, when Chaim was a boy. Let’s see:
There was a total eclipse of the sun in the region of Bialystok on September 7, 1820, when my grandfather was ten years old, a date which would bear eloquent testimony to his precocity.
A German astronomical expedition was set up on the site; shiny telescopes adorned the landscape; the weather was perfect for the observation of the celestial phenomenon. The villagers looked with apprehension mixed with wonder at the primly dressed German scientists.
My grandfather, then a boy of tender years, watched the proceedings with unabated curiosity. A German astronomer was moved to speak to him (the Yiddish-speaking natives could understand elementary German without difficulty). ‘The sun will gradually become smaller and smaller, and soon it will be completely blotted out. But you must not be afraid,’ the German reassured the boy. ‘After a few minutes of total darkness, sunlight will return.’ My grandfather listened to the German’s explanations with due respect, and then said, in passable school German: ‘I know all that. What I cannot comprehend, however, is how you expect to make any worthwhile observations of the corona without a double diffraction lens.’ The German was startled. ‘Where did you learn all this?’ he asked in utter astonishment. ‘Why, every street urchin in the village knows such elementary stuff,’ was the reply.
The astronomer dispatched a report to the Berlin Academy of Sciences, in which he declared that Bialystok was the most civilized community in the world, and he advanced the theory that this extraordinary state of knowledge amid a largely illiterate population was due to the preservation through the centuries of secret rabbinical doctrines dealing with celestial phenomena.

According to custom, peculiar to the Eastern European Jews, to unite the children early in wedlock, Chaim’s marriage was arranged when he was only sixteen, and on his eighteenth birthday, he was given a wife. She was Reiza Rivhas Neches (probably his distant relative) from Zabludow (a small town with a large Jewish community near Byelostok). As usual, the father-in-law took the young couple to his wooden house, located in the market of Zabłudów (where he had a grocery), to pass there the first part of their married life. Chaim and Reiza soon had two daughters.

In Zabludow the teenager continued his rabbinical studies, but his attention was soon attracted by Maimonides’ treatise Kiddush Hachodesh, and its calculations and astronomical observations captivated his mind. Then he came across the Naaveh Kodesh of Rabbi Shimon Waltosh, a treatise on geometry, trigonometry, and stereometry, and mastered it for a short time. The next was the Hebrew translation of Elements of Geometry of Euclid by Rabbi Baruch Sclower, then the Shebilay Derakiah of Rabbi Elijahu Heches, a rare mathematical treatise, then the Euler’s Algebra, then the Mennig’s Cursus of Mathematics, in four volumes (he needed two months to finish this ponderous work). Another opportunity brought him together with a pharmacist in Bialystok, who volunteered to teach him German.

In 1831 the three years, during which time his father-in-law had engaged to support him and his family, were passed, and being without means, and without any business, dreary prospects were before Chaim. Nothing remained for him than to accept the place of bookkeeper with his brother, who owned a glass manufacture, some 60 km from Bialystok, deep in the woods. For a year and a half, every hope of progress was taken from him, no book, a lot of boring work. Fortunately, he found the mathematical works of Abel Berrias in eighteen volumes, and in the deep hour of the night only was he able to pursue his beloved studies.

Sometime in 1831 or 1832, knowing that the Jewish literature had no works in that line, and that the Eastern European Jews had no opportunity to study mathematical works in a foreign language, Chaim undertook to write a whole course of mathematics, both the pure and applied, in the Hebrew language. Thus he wrote a manuscript, Mosede Hokmah (On the Principles of Mathematics), but nobody would have ever heard of that hidden knowledge if a kind Providence had not furnished him an opportunity. In 1833 his brother sent him on a business trip to Grodno, the governorate center. There Chaim met Eliezer Rosenthal (1794-1868), a famous Jewish book collector, who encouraged him and advised him to go to Wilna (Vilnius, the capital of modern Lithuania), where there is a Jewish printing office and a host of learned men, who will help him to get his works published.

Thus in 1834 Slonimski traveled to Wilna and asked for financial support from the first men of the local Jewish community. A subscription list was opened, but by reason of the poverty of the Jews it had not much success. The printers were not enterprising enough to take hold of a new work in Jewish literature. The expenditure of a thousand roubles appalled them, and thus Chaim was forced to publish only one part (which treats of Algebra) of his great work.

From Wilna Slonimski went to Minsk, where the young mathematician enjoyed the most marked attention, and encouraged by his first success in mathematics, he returned to Zabludow. Although he drew upon himself already, by the publication of scientific works, the name of a Berliner (sectarian), as they called him tauntingly in his small town, and although his wife felt greatly chagrined by the danger which the orthodox reputation of her husband run, yet she relaxed in her opposition, when the silvery sound of 75 roubles struck upon her ear. A year and a half he passed now under his domestic roof, enjoying greater freedom for study. He ordered several books from Leipzig, for a pamphlet on Halley’s comet, which he intended to publish.

Thus in 1835 Slonimski released Sefer Kukba di-Shebit, a collection of essays on the Halley comet and other astronomy related topics such as the laws of Kepler and Newton. This work significantly increased his popularity, because Halley’s comet was a widely discussed topic as the return of this periodic comet was expected in 1835. Rapaport, Reggio, Geiger, and other scholars, began to correspond with him, and from all parts, he received encouraging words.

In 1836 Chaim Zelig visited again Wilna and Warsaw, where he passed a few weeks with the mathematician Abraham Stern, and went from there to Königsberg. Stern, a prominent member of the local community, became his patron.

When in 1836 Slonimski returned to Zabludow, his domestic troubles got worse and worse (his wife’s family was against his scientific pursuits), and only the last remedy, so frequently used among the Polish Jews, remained to him, to divorce himself from his wife. Deprived of all means and the only support for his small children, at the end of 1836 he returned to Bialystok, his native place, and poverty in all its nakedness starred him in the face.

But his ill-luck had reached its climax, and fortune began from now to smile on him. Abraham Stern got information of his misfortune, and with parental kindness, he invited Slonimski and his family to his house in Warsaw, and highly recommended him to the local Jewish community. Thus Slonimski obtained a permanent situation among the numerous beneficial societies of the Polish capital and get the support of Itshak Shimon Rosen, a prominent banker.

Moreover, later Stern offered him the hand of his youngest daughter, Sara (Salomea) Gitel (1824–1897). Thus in early 1842 Slonimski married Stern’s beloved daughter. They had five children: Abraham Jakub (1845-1849), Leonid Ludwig Zelig (1 Nov. 1849-1918), Michal (b. 1850), Stanislaw (1853-1916), and Josef (1860-1934).

In 1838 Slonimski’s work on astronomy, The History of the Heavens, appeared in Warsaw with introductions in Polish by two prominent Polish astronomers.

Financial troubles constantly plagued Slonimski, and the ability to organize his affairs was completely alien to him. In the late 1840s by a stroke of luck, he managed to sell the rights of the manufacture of his adding machine to England for £400, a huge sum for the time. He invested the money in the acquisition of a fruit orchard in the town of Tomashov, and engaged in gardening and making experiments in the preparation of pottery on a new method invented by him.

In the 1850s and 1860s, Slonimski continued his scientific pursuits. In 1853 he invented a chemical process for plating iron vessels with lead. In 1856 he designed an electrochemical device for sending quadruple telegrams, which enabled simultaneous double transmission and reception—four active communication channels were open through one wire at the same time. In April 1858, he addressed a letter to the Directorate of the Russian Ministry of Transportation, in which he revealed a thorough understanding of the processes that take place in duplex telegraphy, and for the first time proposed a method to obviate certain difficulties of simultaneous transmission of messages over the wire. Despite the novelty of his proposal and the feasibility of its practical application, he failed to obtain the necessary funds for his experiments. In 1859 Slonimski published a separate brochure containing a detailed description of his method. The system of multiple telegraphy, which was used by Lord Kelvin in 1858, was based on Slonimski’s discovery. Later, the same invention was repeated by Thomas Edison, who could hardly have known anything about Slonimski’s work.

In 1863 Chaim Zelig Slonimski was appointed government censor of Hebrew books in Zhitomir and was named inspector of the rabbinical seminary (a government-sponsored rabbinical school). He served as an inspector for 12 years, until the Russian authorities closed such seminaries down.

First in history, Slonimski began writing and publishing science books in Hebrew to enlighten the Jewish population in Eastern Europe. He started publishing a popular science magazine, Ha-Zefirah, 1862, in Hebrew, which continued after his death, till 1931. Ha-Zefirah was a cultural event of prime importance in the Jewish community because of the vast amount of miscellaneous information that was generously spread across its pages. Until the last decade of the 19th century, Slonimski strove to develop a broad Jewish scientific discourse that would be accessible to as many educated Jews as possible.

Chaim Zelig Slonimski was an idealistic, but impractical genius. Let’s look at how he is described in the Энциклопедический словарь Брокгауза и Ефрона (The Brockhaus and Efron Encyclopedic Dictionary is a comprehensive multi-volume encyclopedia in Russian), published in 1900 (one of the editors of this encyclopedia was his son Leonid Ludwig), when he was still living:
The mathematical gifts and inventive power with which Slonimski astounded both theoretical and practical scientists in his youth, were not exploited by him in full, partly because of the unfavorable living conditions of Russian Jews and partly because of Slonimski’s own intellectual idiosyncrasies. Once he had found the solution of a specific problem…, he was in no hurry to publish his findings… and often laid them aside for many years until the foreign scientific periodicals announced these inventions as new accomplishments of some Western scientist.

Chaim Zelig Slonimski carried on in excellent mental and physical health well into his tenth decade (he inherited his longevity from his grandfather, Yehiel Neches, who also lived to 95, and his grandchild, the composer Nicolas Slonimsky, died in 1995 at the age of 101). He died on 15 May 1904, in Warsaw. His gravestone in the Jewish cemetery on Okopowa str. in Warsaw is still preserved (see the nearby image).

David Roth (1808-1885) was an Austrian Jew and Parisian doctor, who around 1840 turned his attention to the design and construction of mechanical calculators. Between 1840 and 1844, Roth registered six patents (totaling 72 pages), as the first patent was registered in May 1840, the last in March 1844. Besides, in 1843, an English patent was registered by David Isaac Wertheimber, his commercial agent in London.

At the French Exposition Nationale in 1844, Roth presented several calculating machines as well as gas meters and was awarded a bronze medal for his inventions. Let’s see an extract from “Report of the Exposition Nationale of 1844”:
Dr Roth presented arithmetic machines that he had invented for the jury to examine; some were intended only for the two first rules, the others, more complete, working multiplication and division as well; he also presented meters for steam machines and other similar devices. None of these machines is new in its intended purpose, but Dr Roth has solved these various problems by simple means worthy of interest. The jury awarded Dr Roth a bronze medal.

We don’t know which is the source of Roth’s interest in calculating machines (probably the upcoming Exposition Nationale of 1844). Interestingly, we know that when in September 1841 Roth visited London to demonstrate his calculators at the Polytechnic Institute, he met Charles Babbage, and the two men discussed the by-then aborted project of the differential engine. However, it seems Roth’s interests in this area only lasted some four years, because after 1844 he switched to most profitable activities, like practicing homeopathic medicine for a rich clientele in Paris.

Roth intended his calculators to be used in the armed forces, in government offices, in business, and also in schools. French Public Works Ministry ordered 12 of them on 29 June 1844, 9 of the ten-digit model, and 3 of the eight-digit model. Roth also noted that by understanding the mechanical workings of the calculator, children would gain a better understanding of arithmetic. Amazingly, for only four years he designed many models of calculating devices, which can be divided into two groups—adders and multipliers.

1. Adders of Roth.
There are many variations of adding machines of Roth (called Additionneur-automate), with different capacities and carry mechanisms (Roth thought up four different systems for tens carry), as quite a few examples (about 20) are preserved in the collection of Musée des Arts et Métiers in Paris. Some devices have no mechanism for resetting to zero. Others have been adapted for foreign markets. There are simple adders and adder-subtractors. But all share the toothed wheel, the double cam, and the lever. Let’s examine one of Roth’s adders.

This type of adding machine of Roth was shown in Vienna in 1842 and 1844 and received a bronze medal at the French National Exhibition of Industrial Products. The Societe d’encouragement pour l’industrie nationale bestowed its silver medal on the adding machine, and it was used by the Navy Department in France.

The instrument is enclosed in an oblong teak box with dimensions 35 x 6 x 1.5 cm. It consists of an upper plate in bronze, pierced by rounded slots through which the toothed wheels of the dials are partially visible. These wheels have twenty teeth on their circumference which correspond to the doubled series of numbers 0.1.2.3.4.5.6.7.8.9.

Jumper springs, made up of a simple flat spring, stop the wheel at each tooth.

On the lid can be inscribed one (for adding machines) or two rows of digits (for adding and subtracting machines). The row outside the slots is used during the addition, while the row below the slots is used during the subtraction (its digits are complementation to 9 of the digits of the upper row.)

The carry mechanism is extremely efficient. Between each pair of wheels, there is an L-shaped lever, fixed on an axle and held by a spring. A double cam underneath each toothed wheel progressively winds up the lever and releases it suddenly. Under the pressure of the spring, the lever acts like a balance and makes the next wheel move forward a notch (one unit).

The mechanism for resetting to zero is equally ingenious. The lower plate has three curved slots over which a flat rod, armed with little pins, moves. When one pulls the rod, it describes a slight semi-circular movement. The small pins act on propeller-shaped pieces which are placed under the double cams. Whatever their position, they are all going to form a horizontal line which, on the dial figures, corresponds to a value of 9. The operator then has only to add one unit with his stylus to pass from 99999999 to 00000000.

Adding machines according to patents of Roth were manufactured in many countries around the world—France, Germany, Russia, England, Japan, etc. They were reliable and very cheap devices. The adders had been manufactured in small series from 1842 and sold at a moderate price (60 F, the price of a two-year subscription to the magazine L’Illustration).

2. Multipliers of Roth.
There are three types of multiplication devices, designed by Roth.

2.1. The circle multiplier of Roth.
The most elaborate calculating machine of Roth is his circle multiplier. In this calculator, he used the pin-wheel mechanism, known from the sketch of Leibniz (around 1670) and machines of Poleni (1709) and Braun (1727), which was forgotten for a long time. Interestingly, almost at the same time (around 1840), another inventor designed a pin-wheel calculating machine (the Polish Jew Izrael Staffel). Roth (just like Staffel) didn’t specify where he found a description of the pin-wheel mechanism, although we can hardly imagine, that a doctor can reinvent such a simple and ingenious mechanism some 170 years after its idea appeared in the mind of Leibniz, one of the most important mathematicians and natural philosophers of the Enlightenment.

The outside circle (so-called totaliser) is composed of a series of nine dials, each with a series of numbers (0-9/9-0). The discs are pierced with 20 holes. The right half is used for addition and the left is for subtraction. The series of numbers are placed semicircular. (They are red for subtraction).

The machine does not have a resetting mechanism. The carry mechanism works like this: there is a series of twenty-toothed wheels on which two series of numbers are engraved in double (complementary numbering). As each tooth corresponds to a unit, it’s not one but two little rods, fixed under the wheel, that are going to act, at each half-turn, on a lever that will move the following wheel forward one notch.

Since the machine is round, the dials are positioned on a curved line, but Roth pointed out that he could have made a straight machine without any problem. Between each dial, and unlike the simple adders, turn counters (quotient) have been added (8 counters). Under each dial, a small gear wheel engages with an eccentric pinion which moves the turn counter (quotient).

The mobile middle section is composed of five registers and a button to change between addition and subtraction. Each register is composed of a series of numbers engraved on the plate, numbered from 0 to 9, a central disc pierced by a single hole, and a window showing the figures on the dial. When the exterior plate is removed, a large 100-toothed wheel can be seen with five smaller wheels on the same axle as the registers. There are also five wheels, called development wheels, based on a pin-wheel mechanism, described by Roth in this way—It’s a copper disc of which one-fifth has nine grooves carved into its thickness. The grooves contain nine movable bolts which, when pushed towards the exterior, create as many teeth but which, when retracted into the grooves leave the edge of the disc perfectly smooth. If one of the bolts is moved out of its groove, the disc has one tooth; it has 2 if two bolts are moved out; nine if all the bolts are out of their grooves. On the other hand, it has none if none of the bolts is out of its groove. Each bolt has a pin in the middle which is acted on by a small inclined plane cut into a moving plate that covers the disc and its grooves. It is thanks to this inclined plane that the bolts are moved out of their grooves and returned.
Imagine now that the five development wheels are placed in a circular line on the lower part of the mobile plate, and that the big central wheel has 100 teeth that engage with the twenty-toothed pinions of the lower part of the development wheels. Imagine the big wheel divided into ten equal parts and it is easy to see that, while it makes one-tenth of a turn, the development wheels make a full turn around their axles.

The big central wheel had one hundred teeth. Imagine that each development wheel has one protruding tooth (i.e. the value 11111 on the registers). If the big wheel makes a tenth of a turn, the development wheels are going to add one unit to each of the totalizers and, therefore, mark 11111. If it makes four-tenths of a turn, the totalizers will show 44444.
The operator indicates the value of the multiplier on a circular dial with a moving pointer placed on the same axis as the crank. When the value is reached, the pointer comes up against a stop hook. The crank never makes a complete turn; a ratchet always makes it return to its starting position.

The moving part (carriage), is in the central section, where the registers are. Quite simply, one releases it by pressing a button. Then one only has to place the first development wheel on the right in front of the unit dial of the outer circle to begin the operation.

To prevent too high speeds in the mechanism, resulting in wheels overturning too far, Roth provided a fly-brake.

2.2. The permanently engaged multiplier of Roth.
The second multiplication device of Roth is the so-called permanently engaged multiplier. This is a multiplier, which is much simpler and cheaper than his superb variable-toothed circular multiplier.

Roth used for this multiplier the construction of the adding device, but added to each dial gear trains which form a series of continuous gearings. Above each dial, eight other dials are arranged vertically and linked mechanically by pinions so that these turn in the same direction and have particularity in that their speed increases progressively by one-tenth from bottom to top. In short, when the top dial (of 9’s) has completed a turn, the 8’s dial will have done 2, etc. and the adder (totalizer) dial will have done 9. Since this one has a carry, the result obtained will be 81.
Imagine it with a capacity of eight figures. It would then have 72 dials, which would not be simple to manufacture.
For each decade there would be nine dials. The lower one is the totalizer dial of the adder. The others correspond to the multiples 2, 3, 4, 5, 6, 7, 8, and 9.

Under the plate and for each multiple there is a 20-toothed dial wheel, armed with a jumper spring, and carrying the numbering 0.1.2.3.4.5.6.7.8.9. 0.1.2.3.4.5.6.7.8.9, two gear wheels with 90 teeth placed one above the other for the 9’s multiple, two 80-toothed wheels for the 8’s multiple, etc. These gear wheels were doubled up, probably for strength reasons. Intermediary pinions also doubled up, have many teeth inversely proportional to the gear wheels to maintain an equal distance between each dial.

2.3. The multiplier and divider with small rulers of Roth.
The third type of multiplication device, designed by Roth is the so-called multiplier and divider with small rulers (Multiplicateur et diviseur à réglettes) (see in the nearby figure the drawing of Multiplicateur in French patent (Brevet d’invention) 16536 dated 18 March 1844). Roth imagined a very ingenious system for multiplying and dividing with small rulers. In this new setup, nine series of figures, one above the other, are printed on a small cardboard ruler.
They show the multiple of each number from 1 to 9. The instrument, with a capacity of 6 figures, has 6 small rulers which overlap partially. Small, carefully positioned cutouts show “the excess of transmission of the unit on ten”. In short, it’s a matter of spreading the product of multiplying one figure by another over two orders of decimals.
The small rulers are placed in a wooden frame, containing nine horizontal windows (for each multiple).
The bottom section has six vertical slots with cursors (knobs) which allow the small rulers to be moved up and down in order from 0 to 9, thus the figures of the multiplicand are entered.

Biographies of David Roth and David Isaac Wertheimber

The Austrian Jew David Roth was born in 1808 in Cassovia (now Košice in Slovakia, but then it was part of Hungary and as such within the Habsburg Monarchy). At this time, Antisemitism was particularly strong in the Austrian Empire (e. g. Jews had to live outside the town), but the Roth family was the only Jewish family who had special permission to live within the town.

David’s father died when he was only ten. His mother Anna, who had a private income, stayed in town since 1814 as a renter and cook for the local kosher restaurant, serving itinerant merchants. It was a profitable establishment or else Anna Roth was clever enough to acquire patronage, possibly from the Jewish community, because all four of her sons studied in Vienna. Two of them, David (1808-1885) and the baby of the family, Mathias (1818–1891) (who in 1849 moved to Britain, where he stayed for the rest of his life, creating a remarkable family), both became well-known physicians and homeopaths. The third brother, Emerich Emanuel (AKA Imrich or Imre Mano Roth) (1814–1885), was trained in Paris and Vienna and became a well-known Austrian painter and photographer. The fourth brother, Felix, became a merchant and stockbroker in Vienna and was awarded the knighthood of the Order of Francis Joseph.

So in the middle 1820s, the young David Roth left Cassovia to study medicine in Vienna. David became a product of the Jewish Enlightenment, being one of the young men who escaped the ghetto culture by embracing the study of the natural sciences.

The Medical School in Vienna (see the lower image) was highly conservative and homeopathic medicine, commended by Samuel Hahnemann, was really not the flavor of the day. It was not authorized until nearly 1829. It was probably during that period that David Roth stood up for this new medical approach.

In 1831, a terrible cholera epidemic struck Austria and Europe, just when Roth finished his studies, and he was sent to work in the rural district of Wieselburg (Mosonmagyarovar) and the estates of Count Zichy-Ferraris. There was panic in the towns. The Jews were accused of poisoning the wells. In Košice and the surrounding area (as in many other places in Europe), cholera triggered violent riots. One of the town physicians was assaulted and very nearly killed. Only the arrival of the militia prevented the Jews from being burnt at a stake already prepared. In the circumstances, one can understand why Roth, a young medical graduate, would decide to leave Austria for a somewhat gentler country.

So in 1831, the young doctor emigrated to Paris, France, with a letter of recommendation from Count Zichy-Ferraris, who was Metternich’s father-in-law, to Baron Rothschild, the Austrian ambassador in Paris. In Paris, he became a well-known doctor of homeopathic medicine (under the name Didier Roth, and under the pseudonym Beauvais de Saint-Gratien) for a rich Parisian clientele for more than 30 years (he treated personalities such as Rothschild, Chopin, and Heine). During the 1840s, he was a staff physician at the Austrian Embassy in Paris.

In France Roth published several medicine books—e.g. in 1832, he published his Health Instructions against Cholera Morbus. He said he had cared for a large number of patients there. Between 1836 and 1840, he published Homeopathic Clinic, an enormous compendium in nine volumes recording nearly 5000 clinical observations. His History of irresistible musculature or normal chorea earned him a medal from the Académie Nationale de Médecine in 1850. His talent for translation (he was fluent in Hungarian, English, French, German, and Yiddish) made him an unavoidable publisher of homeopathic thinking in Europe.

It is unknown what was the primary reason for the reputable doctor to leave the homeopathic circle around 1840 to invent calculating machines. Most probably he was inspired by the French National Exposition (Exposition Nationale) of 1844. Between 1840 and 1844, Roth registered six patents—totaling 72 pages. Another famous inventor, who also presented several calculating machines was an outstanding figure in the industry of mechanical calculators—Thomas de Colmar. Roth certainly had been acquainted with the machines of Thomas, as can be seen by the descriptive memo, serving as a prelude to his second patent of 18 June 1841.

It seems that after the remarkable primary success of his calculating devices, in the late 1840s, Roth gave up mechanics, continued practicing homeopathic medicine for a rich clientele in Paris, and indulged in his new passion: art.

David Roth was very passionate about art and managed to build up a very beautiful collection of old engravings, notably by Dürer, which are now kept in the Bibliothèque Nationale in Paris. In the 1860s he became an inescapable art consultant for the Rothschild family, whom he served as a family physician. Artistically gifted, he prepared copper plates for bank notes that would have been less easily forged than those in circulation. He also designed clocks and various bronze ornaments.

David Roth was married to Anne Nathalie Sassary, but they had no children. He did have a stepson from Nathalie Sassary, who died in the 1870/1 revolution. Nathalie died in 1878.

With age, his sight deteriorated and at the end of his life, David Roth became completely blind. His last years he spent as a recluse, still working on his art collection and playing the piano. This extraordinary man died on 25 December 1885 and was buried in the Montmartre cemetery in Paris, along with his wife Nathalie and his stepson.

Little is known about the Parisian merchant David Isaac Wertheimber, who in 1843 patented in London the pin-wheel calculating machine of Roth. He was mainly known as the father of the famous French middle 19th-century contralto Palmyra Wertheimber (born in Paris on 9 September 1832, died Paris 12 March 1917). David Isaac Wertheimber was a German Jew, born in Bayreuth, Bavaria, in September 1793 and died in Paris on 11 July 1881. He married Esther Lanzenberg (Strasbourg, Bas-Rhin, 3 August 1808 – Saint-Aubin-sur-Mer, Calvados, 23 July 1903), in Strasbourg on 3 September 1827. They lived in Paris and had (at least) six children: Léo (born 11 March 1829), Henry (b. 19 March 1830), translator, Mina (b. 8 August 1831), Palmyra (1832-1917), Noémie ( b. 1 July 1834), and Flavie (b. 22 May 1842).