Lanz, José María De

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(b. Campeche, Mexico, 26 March 1764; d. Paris, France, c. 1839),

abstract theory of machines, classification of machines, mechanisms design, naval sciences, scientific exploration.

Lanz belongs to an exceptional generation of Spanish exact scientists, all born in the 1760s. Most of them joined the Spanish Royal Navy, and several were later sent to Paris to acquire further experience in science or engineering. In Paris, Lanz worked at national scientific projects and became a professor at the École des Géographes. In 1808 Lanz wrote a seminal book on an abstract classification of mechanical machines. Later he moved to his native Spanish America, playing a leading role in the transmission of the exact sciences to Argentina and Colombia. In Paris, where he returned, he was associated with the firm founded by his friend, the clockmaker Abraham-Louis Breguet (1747–1823).

Origins and Studies . José María de Lanz was born in Campeche, Mexico, where his Spanish father had moved on crown business; on both sides his family had a long Basque ancestry, a connection that would have some relevance in his life.

At the age of fourteen he was sent to Spain to be educated at the Real Seminario in Bergara, in the Basque country. This was a newly established institution for the training of the young nobility, with a definite emphasis on areas of science and technology, perhaps with a view to a more efficient exploitation of natural resources in America. The chemical element Wolfram (or tungsten) was first isolated in Bergara in 1873, and large-scale techniques for the purification of platinum were also developed there; the chemist Joseph-Louis Proust (1754–1826) taught in Bergara by the end of the 1770s.

Work in Spain and France . Around 1780 the Spanish navy supported an observatory and an outstanding group of scientifically oriented officers at its naval base near Cadiz; they were attempting to develop technical facilities relevant to navigation and naval warfare. Graduates from Bergara’s Real Seminario had the privilege of joining the navy immediately after graduation; this is the route Lanz followed. He became a Guardia Marina in 1781 and in the following two years received further naval training, seeing action in naval combat against Great Britain at a time when Spain had the support of France. In 1783, already an Alférez de Fragata, he was sent to Cuba and Mexico to report on vegetal fibers used to make ropes for naval use.

In 1784 Lanz started a new stage in his navy life: He was moved to the scientific navy unit near Cadiz, joining an elite cartographic unit. At the time the eminent astronomer and mathematician Joseph de Mendoza Ríos, later a member of the Académie des Sciences, Paris, and of the Royal Society, London, was planning the creation of a more advanced scientific institution within the navy, and in 1788 chose Lanz, then his protégé, as his assistant for a two-year journey through Europe, in 1789–1791. The purpose of this journey was to evaluate new scientific techniques of interest to the navy that were being developed outside Spain, as well as to buy new books, tables, maps, and instruments. During this commission, which was later extended, he worked on problems of mathematics related to the calculation of mathematical tables. He also wrote a treatise on infinitesimal calculus.

Back in Madrid in July 1792 he requested permission to return to Paris, which was denied because of the possibility of a war with France. Disobeying his orders, and expecting permission would be granted later, he returned to France, where he married, probably in October that year. In 1794, after long deliberations, as his talent was widely recognized, his name was struck from the navy list. There were, however, other reasons recommending his removal from the navy: Lanz had become a supporter of the ideals of the French revolutionaries; officially, his defection was attributed to his marriage to a French woman.

In a rapidly changing world, the political situation in Spain changed, and Lanz’s sins were forgotten; however, he was never reinstated to the navy. He was invited to return to Madrid, which he did for a short period in 1796. In that visit he acquired new powerful political friends. Back in Paris he worked on calculations for Gaspard Riche de Prony’s mathematical tables project, of considerable interest to the navy; he also was a professor at the École des Géographes from 1796 until 1802, when the school was closed.

In 1802 Lanz returned to Spain as a professor of the newly founded Escuela de la Inspección General de Caminos, later Escuela de Caminos y Canales, modeled on the Paris’ École des Ponts et Chaussées. There he worked under the Spanish engineer Agustín de Betan-court (1758–1825); in 1806 he returned to Paris on a one-year leave of absence.

The Essai sur la composition des machines . His celebrated Essai sur la composition des machines was published by the École Impériale Polytechnique in 1808 under the authorship of Lanz and his Madrid chief, Betancourt. The reversal of the alphabetic name of authors suggests that Lanz had the larger responsibility in the making of this work; later editions of the Essai were updated by Lanz alone. In this book, his main work, he attempted to present an abstract classification of machines based on the composition of a limited number of “atomic” or elementary machines. He followed the linguistic ideas of Étienne Bonnot de Condillac (1715–1780), already adapted by Antoine-Laurent Lavoisier, Carl von Linné, and others to different scientific contexts. The idea of finding the “atomic” components of machinery was first advanced by Gaspard Monge (1746–1818) and sketched by his student Jean N. P. Hachette (1769–1834). For a good part of the nineteenth century Lanz’s book remained an important source; in the early twenty-first century it is considered a classic. Lanz was short-listed for nomination as a corresponding member of the Académie des Sciences, Paris, in 1811 and again in 1813, but was not elected; on both occasions, the scientists considered were internationally renowned.

Back in Spain . In 1809 Lanz returned to Spain, where he worked in different technical departments under Joseph Bonaparte, imposed as king of Spain after the French invasion. From late 1809 to early 1810 Lanz was in Madrid as director of the Conservatorio de Artes y Oficios and, briefly, also of the Servicio Hidrográfico; in 1811 he served as town governor of Córdoba. By the end of 1812, as French troops retreated from Spain, he moved back to France.

Lanz was an afrancesado (Francophile), a name reserved in Spain for supporters of the Enlightenment and, later, of the French Revolution and Napoleon. They included a good part of educated Spaniards of the time. Among them was the Colombian-born botanist Francisco Antonio Zea (1770–1822), director of Madrid’s Botanic Garden and a friend of Lanz.

Scientific Work in Latin America . In 1816, either in London or in Paris, Lanz accepted an invitation of Bernardino Rivadavia, future first president of Argentina, to move to Buenos Aires as a professor of mathematics and mechanics. There he founded a mathematical institute with a modern organization, which should be regarded as the true origin of advanced mathematics teaching in Argentina. A year later, back in France, he worked for the reconciliation of Spain and independent Argentina, but with little success. He reestablished contact with Zea, who was then in touch with Simón Bolivar (1783–1830) and other Colombians and Venezuelans working for the independence of the countries at the north of South America, so-called Grand Colombia. Diverting funds from a loan obtained in London for the repayment of war debts, Zea recruited Lanz as head of a scientific and cartographic expedition. Possibly with the help of Alexander von Humboldt, Lanz assembled a formidable group of young scientists eager to help the new republics and study their natural world; they moved in strict secrecy to Colombia in 1822. Among others in that group was Jean Boussingault (1802–1887), who later became a member of the French Académie des Sciences in Paris and a world leader on agricultural chemistry; in his memoirs he referred to Lanz with affection and respect. As a result of their work, important new maps, some compiled by Lanz himself, and more accurate descriptions of fauna, flora, and minerals in the area became available. One of Zea’s goals in financing this work was to attract the attention of European investors to the wealth of his country. The expedition also stimulated interesting institutional developments in science and engineering in Colombia, and the creation of an academy of science in Bogotá.

Lanz remained in Colombia for some two years, but his health was affected by Bogotá’s altitude and he was forced to return to France in 1824. From Paris he worked as an agent of the Grand Colombian government, trying to negotiate France’s recognition of its independence. From intense discussions at the highest levels of government, which involved the president of the council, or premier, Joseph de Villèle (1773–1854), and the foreign minister, Ange-Hyacinthe-Maxence Damas (1785–1862), it became clear to Lanz that, at the time, the French government, even if sympathetic to open commerce with the new republics, could not possibly recognize the independence of Colombia before Spain, or at least Great Britain, did so. This view was probably misinterpreted in Colombia, and Lanz was relieved from his duties in Paris in 1826. He did return to Colombia, where he had been made a colonel in the army, a frigate captain in the Grand Colombian navy, and a member of the new academy of science. As with so many other personalities of the time, Lanz had Masonic connections; possibly, this was mainly a line of personal communications and contacts in Europe and America.

Last Years in Paris . After breaking with Colombia, Lanz lived modestly in Paris, possibly designing mechanisms for Bréguet’s works. In the early 1830s, when changes began to take place in Europe, he attempted to return to Spain. In 1832 he applied for a teaching position at the Conservatorio he had helped to create in Madrid; those charged with judging applications dismissed his, alleging he was unknown.

He died, possibly soon after his wife, his life companion, toward the end of the 1830s, possibly around 1839. No picture of him seems to have survived. However, Lanz has been described at various times in his life, and in different countries, as a deeply intelligent man, sensible, with a sense of humility and dignity, and as a trustworthy friend. Even in Paris police reports he is described as respectful man with deep and elevated convictions.


Primary sources for the works of Lanz are: Archivo General de Indias, Seville, Spain; Archivo Histórico Nacional, Buenos Aires, Argentina; Archivo Histórico Nacional, Bogotá, Colombia; Archivo Histórico Nacional, Madrid, Spain; Archives Nationales, Paris, France; Archivo General de la Marina Álvaro de Bazán, Viso del Marqués (Ciudad Real), Spain; Archivo Naval, Madrid, Spain; Archivo de Simancas, Simancas, Valladolid, Spain; Archivos de la Universidad de Buenos Aires, Buenos Aires, Argentina; Bibliothèque de l’Institut, Paris, France; Bibliothèque Nationale, Paris, France; Bureau des Longitudes, Paris, France; Quai d’Orsay, Paris, France.


Essai sur la composition des machines. Paris: L’Imprimerie Impériale, 1808. English translation: Analytical Essay on the Construction of Machines (London: Ackermann, 1820).


Bret, Patrice, and Eduardo L. Ortiz. “On Lanz’s Numerical Work in M. de Prony’s Project.” Revista de Obras Publicas 3305 (1991): 63–66. García Diego, José-Antonio. En busca de Betancourt y Lanz. Madrid: Castalia, 1985.

García Diego, José-Antonio, and Eduardo L. Ortiz. “On a Mechanical Problem of Lanz.” History of Technology 5 (1988): 301–313. A discussion on a mathematical manuscript by Lanz on the reversible pendulum.

Ortiz, Eduardo L. “Mathematics in Spain, Portugal, and Latin America.” In Companion Encyclopedia of the History and Philosophy of Mathematical Sciences, edited by I. Grattan-Guinness, Vol. 2. London: Routledge, 1994. A brief overview of the exact sciences in the Spanish- and Portuguese-speaking world in Lanz’s period.

———. “Geometría, lógica y teoría de las máquinas: El ensayo de Lanz y Betancourt, de 1808, sobre la teoría de máquinas.” Fórmula, Société d’Études Basques 5 (1999): 261–272. A technical discussion on the Essai.

———. “Joseph de Mendoza y Ríos: Teoría, observación y tablas.” Gaceta de la Real Sociedad Matemática Española 4, no. 1 (2001): 155–183. A discussion of the problems considered by Mendoza y Ríos’s and Lanz’s Cadiz group.

———. “Joseph de Mendoza Ríos.” In Oxford Dictionary of National Biography: In Association with the British Academy; From the Earliest Times to the Year 2000, edited by H. C. G. Matthew and Brian Harrison, Vol. 37. Oxford: Oxford University, 2004.

———. “Babbage and the French Idéologie: Functional Equations, Language, and the Analytical Method.” Episodes in the History of Modern Algebra (1800–1950), edited by Jeremy Gray and Karen Hunger Parshall, chapter 2. Providence, RI: American Mathematical Society, 2007. A discussion on the philosophical background supporting the approach used in Lanz-Betancourt’s Essai, and in similar classification attempts.

———, and Patrice Bret. “José María de Lanz and the Paris-Cadiz Axis.” In Naissance d’une communauté internationale d’ingenieurs: Actes des Journées d’étude, 15–16 décembre 1994, edited by Irena Gouzévitch and Patrice Bret. Paris: Centre de Recherche en Histoire des Sciences et des Techniques, Cité des Sciences et de l’Industrie, 1997. On Lanz in France.

Eduardo Ortiz