Thomson and Tait, Treatise on Natural Philosophy, §§318–330: varying action and least action
Source: Internet Archive
treatiseonnatura01kelv_0; local OCR excerpt.txt, lines 25284–29734 of the archive’s_djvu.txt, retrieved 2026-09-08. Metadata: William Thomson and Peter Guthrie Tait, Treatise on Natural Philosophy, Part I, second edition (Cambridge: Cambridge University Press; first edition 1867, second edition 1879, reprinted 1890 and 1895). The scan’s front matter names Cambridge University Press; the printing year is to be read from the title page. The sections belong to Chapter II, Dynamical Laws and Principles. Extraction: archive.org OCR; marginal keywords such as “Least Action” are interleaved with the text and displayed formulae are fragmentary. Section 319, on Hamilton’s method, is long and contains most of the excerpt. Rights: public domain.
Source digest
Sections 318–325 present Hamilton’s characteristic function, the law of varying action and its applications, and §§326–330 present Maupertuis’s principle of least action. Section 327 states it as: of all the sets of paths along which a conservative system may be guided from one configuration to another with the sum of its potential and kinetic energies equal to a given constant, the one for which the action is least is such that the system, started with the proper velocities, moves along it unguided.
For this project, this is the standard nineteenth-century English textbook statement of the fixed-energy principle, placed beside Hamilton and Jacobi; it fixes the action as twice the time integral of the kinetic energy and keeps the energy constraint explicit.
Passage anchors
- Archive line 28551, §326: “Maupertuis’ celebrated principle of Least Action”.
- Archive line 28657, §327: the statement paraphrased above.
- The excerpt begins at §318 and ends before §331.
Coverage and limits
Reading level passage for §§326–327 on OCR text;
metadata for the remaining sections. The section wording
needs a scan check for punctuation.