Tito Gonnella

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

The Italian physicist, mathematician, and inventor Tito Gonnella (1794–1867), professor of mathematics and mechanics at the Florentine Accademia di Belle Arti di Firenze, is primarily known as the inventor (in 1824) of one of the first planimeters (an instrument for measuring the area, enclosed by an irregular closed curve) in the world. An improved version of Gonnella’s orthogonal planimeter was exposed at the London International Exhibition of 1851 in Crystal Palace and received the highest award for this type of instrument—the Council Medal.

Remarkably, besides his prized planimeters, Gonnella devised two calculating machines, and examples of them survive today, the first in Bonn (Arithmeum Museum), the second in Florence (Museo Galileo).

The presentation of Gonnella's adding machine in the catalog of Great London Exposition 1862
The presentation of Gonnella’s adding machine in the catalog of Great London Exposition 1862

We don’t know when exactly Gonnella created his calculating machines, but the first of them—the dial adder, was created for sure before 1857 because in this year he donated one of them (it seems he made three examples) to Leopold II, Grand Duke of Tuscany, who founded his researches. In 1861 Gonnella was awarded a medal for his two adding machines at the first Italian National Exposition in Florence. In 1862, one of his adding machines (the dial adder) was presented at the Great London Exposition (see its description in the catalog on the nearby image), and received an honorable mention For the ingenuity and simplicity of the construction of his calculating machine (In Class XIII.—Philosophical Instruments and Processes depending on their Use; Section: Calculating Machines.) Both Gonnella’s adding machines were exhibited several times in Italy in the second half of the 19th century.

Interestingly, there is a letter from Gonnella to Filippo Corridi, president of the Tuscan Academy of Arts and Manufacturing (Accademia Toscana di Arti e Manifatture), dated 26 February 1859, in which Gonnella complained that the academy had ignored two calculators he invented and built between 1857 and 1859, but acknowledged the arithmetical machine of a certain Count Niccola Guinigi (another Italian inventor of calculating machines).

The two above-mentioned adding machines are described with details in Gonnella’s 35 pages brochure Descrizione di due macchine aritmetiche per l’addizione, published in March 1859 in Florence (see the book of Gonnella, courtesy of Museo Galileo, Florence). Gonnella was obviously interested in calculating devices for many years, as can be seen in his earlier brochure Opuscoli mathematici nei quali si tratta, published in 1841 in Florence (most of the work is concerned with a theoretical treatment of optics, but the final section describes an integrating machine—a form of planimeter).

1. Gonnella’s stylus-operated dial adder

Gonnella's Dial Adder (© Arithmeum Museum in Bonn)
Gonnella’s Dial Adder (© Arithmeum Museum in Bonn, Germany)

The first calculating machine described by Gonnella is a stylus-operated dial adder, based on the idea of Pascaline and several other simple early adders, e. g. that of Jean Lépine and Hillerin de Boistissandeau from the 1720s, but as a realization more akin to the later adding machines of David Roth, and Chaim Zelig Slonimski from 1840s. It seems only one example of the device survived to our time, and it is kept now in the collection of the Arithmeum Museum in Bonn, Germany (see the nearby photo).

The dial adder of Gonnella (see the lower drawing from his 1859 book) is an 8-positional (both in the input and result mechanisms, although the adder presented in London in 1862 was 6-positional) brass and iron device, placed in a wooden box. Its dimensions are 53 x 10,6 x 10,7 cm, weight: 4,5 kg. The numbers are entered by means of a stylus (pen).

The drawing of Gonnella's Dial Adder from the book Descrizione di due macchine aritmetiche per l'addizione
The drawing of Gonnella’s Dial Adder from the book Descrizione di due macchine aritmetiche per l’addizione

The tens carry transfer mechanism of the adder is unique and original, but not quite reliable because in the case of ripple carry (for example adding 99999 plus 1) it tends to jam. Gonnella acknowledged this flaw and attempted to correct it with an anti-jamming device, but we don’t know if such improvement has been implemented.

Interestingly, the Arithmeum model is most probably not one of the first three examples, mentioned to be made by Gonnella by 1859, because despite the similarities between the published drawings and the model, there is a substantial difference. That is the knob at the lower center of the dial plate, destined to help carry transfer, much like the anti-jamming buttons of Guinigi. This device was neither mentioned in Gonnella’s 1859 book nor shown in the published drawings, so it seems possible that Gonnella’s adder was also subject to the ripple-carry problem and was later improved by adopting this patch solution, perhaps influenced by Guinigi’s design.

2. Gonnella’s Keyboard Adder

The Gonnella’s Keyboard Adder, devised probably in 1858, is one of the earliest keyboard-driven machines, after these of White (early 1800s), Torchi (1834), Schwilgué (1844), Parmelee (1850), Schilt (1851), Hill (1857), and Castle (1857). Gonnella certainly was not aware of the machines of the American inventors Parmelee, Hill, and Castle, but he probably knew the machine of his compatriot Luiggi Torchi, which has been exposed in the Palace of Science and Arts of Brera in the 1830s, as well as with the machine of Schwilgué and especially with Schilt’s, which has been exposed at the 1851 London International Exhibition (where Gonnella’s planimeter was awarded) and received a bronze medal.

The Gonnella’s Keyboard Adder (see the lower image) is a solid brass-iron device (size 20/30/18 cm, weight below 1 kg).

Gonnella's Keyboard Adder (Museo Galileo—Florence)
Gonnella’s Keyboard Adder (© Museo Galileo—Florence)

The device has a nine-digit keyboard (keys 1—5 on the lower row, 6—9 on the upper row). The accumulator is in the form of a helical drum (a drum with an engraved helix curve). Like other machines of this kind (so-called single column adders), it 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 a 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.

Each of the keys is attached to a toothed sector, the number of teeth of which corresponds to the figure, engraved on the key. The pressing of the keys causes the same upward movement of the corresponding sectors. During this movement, the teeth of the sector will engage with one of the nine tooth wheels and will rotate it, as the angle of the rotation is proportional to the number of the teeth, e. g. pressing of the 7-key causes the corresponding wheel to rotate 7/25 of the turn (because the 100-divisions helical flange of the drum is a four-turns, i. e. 25 divisions per turn).

The teeth wheels are fixed to a shaft, to which is also attached the drum in the left part, on the surface of which is engraved a four-turns helical flange, graduated with 25 divisions per turn (total of 100, from 0 to 99). Thus the drum rotates simultaneously with the teeth wheels. The helical flange engages with a peripheral slit on the bottom of the horizontally mounted wheel (graduated on the periphery 0 to 5), that rotates 1/25 of the turn every turn of the drum, thus counting the hundreds when 99 is exceeded. This solution allows sums up to 599 to be calculated, not requiring a carry mechanism to be implemented, because the addition sum can be read as a combination between the figure on the horizontal wheel and the figure on the drum.

The drawing of Gonnella's Keyboard Adder from the book Descrizione di due macchine aritmetiche per l'addizione
The drawing of Gonnella’s Keyboard Adder from the book Descrizione di due macchine aritmetiche per l’addizione

The above-described mechanism is workable, but it has some shortcomings, which Gonnella surely noticed, that’s why in his brochure he described several improvements, which he obviously never attempted to implement in practice. Some of these improvements are:
1. A mechanism for resetting the drum and the horizontal wheel.
2. A spring-driven arm, destined to avoid the recoil of wheels.
3. A five-key keyboard, to be pressed two in sequence for digits greater than 5.

Biography of Tito Gonnella

Tito Filippo Giovanni Battista Gonnella was born on 18 September 1794 in Livorno, a port city on the Ligurian Sea on the western coast of Tuscany, Italy. He was the son of Francesco Gonnella and Violante Stoppioni.

Francesco Gonnella (1757-1835) was an heir of a known local family. His father, Filippo Maria Gonnella (1722-1798) was a Doctor of Law from the University of Pisa and was known as one of the publishers (in the 1770s) of the famous Livornese edition of Encyclopédie ou Dictionnaire Raisonné des Sciences, des Arts et des Métiers of Diderot and d’Alembert.

Francesco Gonnella was born on 22 February 1757, in Livorno. Just like his father, he also managed to get a Doctor degree from the University of Pisa, and entered public administration, becoming assistant director of the archive of Libro detto delle Riformagioni in Livorno. Francesco Gonnella died on 28 December 1835.

Tito Gonnella, just like his father and grandfather, get a Doctor degree from the University of Pisa. He graduated in 1818, with a treatise on the production of divisions for mathematical instruments. In the same 1818, he was assigned to a Florentine commission which, at the request of Grand Duke Leopold II, was to draw up the new land registry for Tuscany.

From 1829 to 1850 Gonnella taught pure mathematics and mechanics at the Accademia di Belle Arti in Florence, then until 1854 pure mathematics. He is primarily known as the inventor of one of the first planimeters (the so-called wheel-and-cone planimeter that used a friction-wheel integrator) in the early 1820s, and also as the inventor of an improved reflecting telescope (presented in 1841).

Tito Gonnella died in 1867 in Florence.

Literature: S. Hénin, Two Early Italian Key-driven Calculators, IEEE Annals of the History of Computing, 2010. n. 1