David Roth

The problem with the world is that the intelligent people are full of doubts, while the stupid ones are full of confidence.
Charles Bukowski

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.

The patent drawing of the adding machine of Roth
The patent drawing of one of the adding machines of Roth

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

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.

An example of the adding machine of Roth
An example of the above-mentioned adding machine of Roth

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).

Additionneur-automate of Roth (1841) (Musée des Art et Métiers)
Additionneur-automate of Roth (1841) (Musée des Art et Métiers)

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 circle multiplier of Roth (© CNAM, Paris)
The circle multiplier of Roth (© CNAM, Paris)

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).

Variable number of teeth (pin-wheel) mechanism of Roth
Variable number of teeth (pin-wheel) mechanism of Roth

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.

The permanently engaged multiplier of Roth (Courtesy Mr. Valéry MONNIER)
The permanently engaged multiplier of Roth (© Mr. Valéry MONNIER)

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.

The patent drawing of Multiplicateur
Under the plate and for each multiple there is a 20-toothed dial wheel, armed with a jumper spring, and carrying the numbering, 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.

Mathias Roth (1818–1891)
Mathias Roth (1818–1891), became a Doctor of Medicine (Pavia, 1840), then returned home for nine years to practice, and in 1849 settled in London, creating a remarkable family of 7 sons and 2 daughters

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.

The Medical School in Vienna, situated in the General Hospital, in the beginning of 1800s
The Medical School in Vienna, situated in the General Hospital, early 1800s

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).