THE PRINCIPLE OF LEAST ACTION

MAUPERTUIS, (PIERRE LOUIS MOREAU DE).

Les Loix du Mouvement et du Repos déduites d'un Principe Metaphysique. [In: "Mémoires de l'Academie Royale des Sciences et Belles Lettres. Année 1746"].

Berlin, Ambroise Haude, 1748. 4to. Later boards. Issued in "Mémoires de l'Academie Royale des Sciences et Belles Lettres. Année 1746", tome II, pp. 267-294. Bound with the orig. title-page and special title to the whole volume II. Title printed in red and. black, with an engraved vignette. Title-page with a stamp (Royal College of Surgeons of England)

First edition of this important memoir, in which Maupertuis set forth his famous principle of "Least Action", his most important scientific contribution. Its influence is so profound and far reaching that many scientists regard it as the most powerful single principle in mathematical physics and place it at the pinnacle of physical science. Max Planck expressed this view as follows: "The highest and most coveted aim of physical science is to condense all natural phenomena which have been observed and are still to be observed into one single principle... Amid the more or less general laws which mark the achievements of physical science during the course of the last centuries, the principle of least action is perhaps that which, as regard form and content, may claim to come nearest to this ideal final aim of theoretical research."


The middle of the 18th century was a tumultuous and interesting time for the development of mathematics and physics. Voltaire had just returned back to France from England, where he had gotten acquainted with the work of Newton and began working on his "Philosophical Letters", the work through which many Frenchmen would be introduced to Newton. In the meantime, Maupertuis had studied Newton intensely and become the leading French Newtonian, and Voltaire sought his advice as soon as he returned to France. Maupertuis was the first to openly advocate the Newtonian theory in the Paris Academy of Sciences and the first on the continent to use Newton's theory of gravitation to determine the shape of the earth, obtaining a result that opposed the Cartesian system. He published his work on the shape of the heavenly bodies in 1732, and thereby helped spread a new science of the greatest importance. This new science was not harmless, however, and the authorities fell over Voltaire, who was propounding it in his philosophical letters; at the same time, Madame du Chatelet became captivated with the new science and began studying with Maupertuis in 1734. To avoid the Bastille, Voltaire went with Madame du Chätelet to her chateau in Cirey, and there he worked on his "Elements of the Philosophy of Newton", which later became so hugely popular. Madame de Chätelet, however, became acquainted with the thought of Leibnitz, probably through letters from Frederick the Great of Prussia, and became fascinated with his thought. She also began reading Bernouilli's work on movement and was totally convinced after having heard from Maupertuis that he also agreed to the correctness of Bernouilli's arguments. While all of these things essential to the history of science at the time were taking place, Frederick the Great was trying to persuade Maupertuis (after advise from Voltaire) to come to Berlin as president of his new academy there. When Maupertuis visited Berlin in 1740, he was captured (by mistake) at the Battle of Mollwitz and taken to Vienna as a prisoner of war. In 1745, however, he did succeed in coming to Berlin, and he was now given the presidency of the "Académie Royal de Berlin". He inaugurated his presidency with an important paper on the laws of motion and equilibrium, in which he discussed the highly debated theories of Descartes and Newton that so vividly took up the scientific circles of France. This paper was entitled "Les lois du movement et du repos déduites d'un principe de métaphysique" [The laws of movement and rest deducted from a metaphysical principle] (i.e. the offered item). The metaphysical principle mentioned in the title was his "principle of least action", his most significant scientific contribution.

In the introduction to the work, he explains that he bases it on the principle that he first presented in a paper in 1744. He further explains that Professor Euler at the end of the same year had published his "Methodus inviendi lineas curvas maximi...", in the supplement of which he adds "cet illustre Géomêtre démontre: Que dans les trajectories, que des corps décrivent par des forces centrales, la vîtesse multipliée par l'elément de la courbe, fait toujours un MINIMUM." (the offered item, p. 1). Maupertuis now adds that this remark has given him great pleasure and that it is a beautiful application of his own principle on the movement of the planets, and furthermore that he, in the present article wishes, from the same source, to draw more truths about this superior and highly important genre. As such, the present article constitutes Maupertuis' most important work on his principle of least action. By discussing Descartes and Newton, he deduces the laws of motion and equilibrium from the attributes of God and proves that these laws express the principle of least action. The principle is also applied to physics, optics and biology. At the same time Euler provided the principle a mathematical formulation, and thereby laid the foundation for future mathematical studies.

"He regarded (the principle of least action) as his own most significant scientific contribution. It states simply that "in all the changes that take place in the universe, the sum of the products of each body multiplied by the distance it moves and by the speed with which it moves is the least possible." (DSB) - "These laws, so beautiful and so simple, are perhaps the only ones which the Creator and Organizer of things has established in matter in order to effect all the phenomena of the visible world." (Maupertuis).

Poggendorff II: p. 85.

Order-nr.: 38695