Mach, The Science of Mechanics, least action and Hamilton’s principle (1893)
Source: Internet Archive, Google Books scan
sciencemechanic02machgoog; local OCR excerpt.txt, lines 17911–18985 of the archive’s_djvu.txt, retrieved 2026-09-08. Metadata: Ernst Mach, The Science of Mechanics: A Critical and Historical Exposition of its Principles, translated by Thomas J. McCormack (Chicago: Open Court, 1893), from the second German edition of Die Mechanik in ihrer Entwickelung (1889; first edition 1883). Chapter III, section VIII “The Principle of Least Action”, pp. 364–380, and section IX “Hamilton’s Principle”, from p. 380. The scan’s title page reads “Copyright 1893”; a 1919 fourth-edition scan was rejected because it contains later additions. Extraction: archive.org OCR with doubled spaces between words and occasional broken words; marginal summaries are interleaved with the text. Rights: public domain.
Source digest
Mach recounts Maupertuis’s enunciation, which he dates to 1747, Euler’s mathematical formulation, and Lagrange’s extension to systems, judges that Maupertuis had “only a vague formula”, and gives his own physical interpretation of the least-action expression before presenting Hamilton’s principle as the stationarity of \(\int(T-U)\,dt\).
For this project, this is a pre-1901 secondary synthesis that places the Maupertuis, Euler and Hamilton sources in one narrative. Mach’s 1747 date refers to the printed Berlin volume; the memoir is for the year 1746.
Passage anchors
- Excerpt line 2 (archive line 17912): “THE PRINCIPLE OF LEAST ACTION”.
- Archive line 18039: “Maupertuis enunciated, in 1747, a principle”.
- Archive lines 18786–18788: “IX. Hamilton’s principle”.
Coverage and limits
Reading level passage for the opening of section VIII;
metadata for the remainder. The German original was not
retrieved.