モーペルテュイの「作用」,オイラーの「労力」 : 十八世紀中葉における二つの最小作用の原理

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  • Maupertuis's "Action" and Euler's "Effort" : Two Principles of Least Action in the Mid-Eighteenth Century
  • モーペルテュイ ノ サヨウ オイラー ノ ロウリョク 18セイキ チュウヨウ ニ オケル フタツ ノ サイショウ サヨウ ノ ゲンリ

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The principle of least action owes its modern formulation to Lagrange (1736-1813), who also related its "pre-modern" history in his Mechanique analitique (1788): Maupertuis (1698-1759) treated it in an ambiguous manner, while Euler (1707-1783) formulated it more precisely. Recent historical studies have shown, however, the difficulty of maintaining this narrative, for these two scholars departed from different problems and reached at different formulations of the principle. In general agreement with these views, this paper emphasizes a further, crucial distinction between Maupertuis and Euler-their usage of the term "quantity of action." When Maupertuis spoke of "quantity of action," he referred to a product of mass, velocity and distance, and his main concern was with the instanteneous change of two bodies colliding. Euler, on the other hand, investigated various "mechanical curves" under the continuous action of forces, searching for a quantity which was minimum to these curves. He realized then that these minimum quantites could be derived from a single one, which he named "effort." Euler did not accept Maupertuis's definition of the "quantity of action" but identified it with the "effort." Although Euler had acquired the idea of "effort" from Maupertuis's earlier work on the "law of rest," Maupertuis himself did not appraise it so highly. They disagreed over what "quantity of action" meant, and their disagreement was related to the kind of physical problems with which they were concerned; before Lagrange's modern formulation, there were two quite distinct principles of least action.

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  • 科学史研究

    科学史研究 48 (250), 77-86, 2009

    日本科学史学会

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