# English translation of Helmholtz' paper: “On the Physical Significance of the Principle of Least Action”

Ueber die physikalische Bedeutung des Princips der kleinsten Wirkung. Journal für die reine und angewandte Mathematik (Crelle's Journal), Volume 100, Issue 2, 1887, Pages 137-166, and Volume 100, Issue 3, 1887, Pages 213-222.

The title in English: On the Physical Significance of the Principle of Least Action.

Has it ever been translated (to English)?

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I just took a quick look at the paper, and the notation is funny - the same letters are used, but with different meanings: the coordinates are $p$ instead of $q$, which in turn is used for the velocities $\dot q$; momenta are $c$ instead of $p$, potentials are $F$ instead of $V$, the Lagrangian is called $H$ and has the opposite sign, ie corresponds to $-L$; kinetic energy is called $L$ instead of $T$; the Hamiltonian is called $H'$ instead of $H$ – Christoph Apr 29 '13 at 13:42
Hi @Gugg. I think the German spelling mistakes (when compared to modern German) in the original German title will generate an endless edit war. Perhaps one should display both the original and a grammatically correct German title? (Also note that Helmholtz spells 'Prinicips' with 3 i's!) – Qmechanic Apr 29 '13 at 18:03
@Qmechanic Hmmm,... NO. :) I think there are no spelling mistakes in the original title. At the time, they were using both Ue's as well as u-umlauts (see the paper itself), but apparently only Ue's in titles. Also "Princips" had been converted to modern-day German (although my German is lousy). The current version proved to be much more useful in Internet search. That is, the misspelling/modernization made it more time-consuming. Also, I don't expect an edit war. Almost certainly, I won't participate. – Kinnisal Mountain Chicken Apr 29 '13 at 18:20
@Qmechanic To your edited comment. The 3 i's: Not in the title, he doesn't. Does he? – Kinnisal Mountain Chicken Apr 29 '13 at 18:27
@Glen The Udderboat: Ups, you're right. That's just a typo of the website. – Qmechanic Apr 29 '13 at 18:30

In English, I've only found this very limited translation by Yourgrau and Mandelstam.

From these facts we may even now draw the conclusion that the domain of validity of the principle of least action has reached far beyond the boundaries of the mechanics of ponderable bodies. Maupertuis’ high hopes for the absolute general validity of his principle appear to be approaching their fulfilment, however slender the mechanical proofs and however contradictory the metaphysical speculations which the author himself could at the time adduce in support of his new principle. Even at this stage, it can be considered as highly probable that it is the universal law pertaining to all processes in nature. . . . In any case, the general validity of the principle of least action seems to me assured, since it may claim a higher place as a heuristic and guiding principle in our endeavour to formulate the laws governing new classes of phenomena.

Perhaps useful for other readers is the full Russian translation in Полак, Л.С. (ред.), Вариационные принципы механики: Сборник статей классиков науки, 1959. There's a djvu file here. The file can be converted to pdf at, e.g., http://www.djvu-pdf.com/. The Russian-translated paper is at page 430ff (pdf-page 434ff).

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In the book "Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein, Volume 2: The Now Mighty Theoretical Physics, 1870 to 1925" you can find, on pages 131-134 some parts are translated.

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Link-only answers aren't really loved here. The main problem is with them that the remote links can die. I would suggest to duplicate its essential content into your answer. – peterh Jul 23 '15 at 19:47
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. – ACuriousMind Jul 23 '15 at 20:09