To Professor Tyndall, Esq., F.R.S.
I READ your “Notes on Scientific History”*2 with great pleasure and satisfaction. I agree perfectly with all you say respecting Mayer’s researches as compared with those of others; in some respects, indeed, I am inclined to go further than you do. Seven years ago I studied the history of the principle of the Conservation of Energy, and arrived at the same conclusion, with respect to the modern development of this theorem, as the one for which you so ably and warmly contend. Your recent disinterested advocacy of Mayer’s claims, and my own conviction that historic truth is the sole object of your research, inspire the hope that the following remarks will be found worthy of attentive perusal.
Descartes,3 so far as I know, was the first to give expression to the thought that whatever is not material must necessarily be indestructible. This non-material something he called “Force,” a word which subsequently had, for a long period, divers and consequently vague meanings.
In Descartes’s Principia Philosophiae (Pars II., § xxxvi.) we find the following:4—“Deum esse primariam motus causam et eandem semper motus quantitatem in universo conservare.
“Motûs naturâ sic animadversâ, considerare oportet ejus causam, camque duplicem : Primò scilicet universalem et primariam, quae est causa generalis omnium motuum qui sunt in mundo; ac deinde particularem, à quâ fit, ut singulae materiae partes motus, quos priùs non habuerunt, acquirant. Et generalem quod attinet, manifestum mihi videtur illam non aliam esse, quàm Deum Ipsum, qui materiam simul cum motu et quiete in principio creavit†,5 jamque per solum suum concursum ordinarium, tantundem motûs et quietis in eâ totâ quantum tune posuit conservat. Nam Quamvis ille motus nihil aliud sit in materiâ motâ quàm ejus modus; certam tamen et determinatam habet quantitatem, quam facilè intelligimus eandem semper in totâ rerum universitate esse posse, quàmvis in singulis ejus partibus mutetur. Ita seilicet ut putemus, cùm una pars material duplò celeriùs movetur, quàm altera, et haec altera duplò major est quàm prior, tantundem motûs esse in minore quàm in majore, ae quantò motus unius partis lentior fit, tantò motum alicujus alterius ipsi aequalis fieri celeriorem. Intelligimus etiam perfectionem esse in Deo, non solùm quòd in se ipso sit immutabilis, sed etiam quòd modo quàm maximè constant et immutabili operetur : Adeò ut iis mutationibus exceptis, quas evidens experientia, vel divina revelatio certas reddit, quasque sine ullâ in creatore mutatione fieri percipimus, aut credimus, nullas alias in ejus operibus supponere debeamus, ne qua inde inconstantia in ipso arguatur. Unde sequitur quàm maximè rationi esse consentaneum, ut putemus ex hoc solo, quòd Deus diversimodè moverit partes materiae, cùm primùm illas creavit, jamque totam istam materiam conservet, codem planè modo, eâdemque ratione quâ priùs creavit, eum etiam tantundem motûs in ipsâ semper conservare.”
Descartes therefore, precisely like Colding,6 bases the proof of his theorem on a divine attribute. The unsatisfactory nature of such a proof is manifest. Are we not equally justified in asserting that the assumption of a constant quantity of motion involves a limitation of divine power? The almightiness of God must manifest itself by actual achievement, new motion must incessantly be created; therefore, assuming with Descartes the indestructibility of that which exists, the quantity of motion must increase.
Every attempt to deduce a natural law from an à priori conceived attribute of God must inevitably be utterly fruitless.
Leibnitz7 was the first to publish, in its proper form, the general theorem of the conservation of vis viva,8 and to demonstrate the same by empirically ascertained and rationally established theorems. He at once opposes Descartes’s views, and introduces the important conception of vis viva. All this will be found in his article in the Acta Eruditorum, Lips. 1686, entitled: “Brevis demonstratio erroris memorabilis Cartesii et aliorum circa legem naturae, secundum quam volunt a Deo eandem semper quantitatem motus conservari, qua et in re mechanica abutuntur.”
In the warm discussion which arose, Leibnitz argued that the assumption of the incorrectness of his views involved the necessity, or at least the possibility of a perpetual motion; which later he urged is manifestly absurd. Colding employs the same argument; and Helmholtz, in 1847, in his well-known work ‘On the Conservation of Force,’9 attributes great importance to his theorem concerning the absurdity of perpetual motion.
John Bernoulli,10 however, gave the clearest exposition of the principle of the conservation of vis viva, as will be admitted after a perusal of his correspondence with Leibnitz (Vivorum cel. G. C. Leibnilii et Joh. Bernoulli commercium phil. et math.), of his “Discours sur les lois de la communication du movement” (Opera omnia, tom. iii. p. 1), and especially of his memoir entitled “De vera notione virium vivarum earumque usu in dynamicis’ (Opera Omnia, tom. iii. p. 239).
Allow me to draw your particular attention to the following two passages of the last-named memoir:—
“§ III. Hine patet vim vivam [quae aptius vocaretur facultas agendi, Gallice le pouvoir] esse aliquid reale et substantiale, quod per se subsistit, et quantum in se est, non dependet ab alio. Unde concludimus, quamlibet vim vivam habere suam determinatam quantitatem, de qua nihil perire potest, quod non in effectu edito reperiatur. Hine sponte fluit, vim vivam semper conservari; adeo ut quae ante actionem residebat in uno pluribusve corporibus, nisi quid in prioribus remanserit. Atque hoe est, quod vocamus conservationem virium vivarum.”
One fact of peculiar interest is John Bernoulli’s assertion that the vis viva which apparently disappears—that is to say, the vis viva which is not employed in external work such as the raising of a weight—may be consumed in molecular work. The following extract from § 9 of the above memoir will establish this point.
“Si corpora non sunt perfecte elastica, aliqua pars virium vivarum, quae periisse videtur, consumitur in compressione corporum, quando perfecte se non restituunt; a quo autem nune abstrahimus, concipientes, compressionem illam esse similem compressioni elastri, quod post tensionem factum impediretur ab aliquo retinaculo, quo minus se rursus dilatare posset, et sic non redderet, sed in se retineret vim vivam, quam a corpore incurrente accepisset; unde nihil virium periret, etsi periisse videretur.”
The conversion of vis viva into heat, or at least the possibility of such a conversion, was first asserted by Augustin Fresnel.11 The French translation of Thomson’s ‘Chemistry’12 contains an appendix “On Light” from Fresnel’s pen, wherein he says:—
“C’est un principe général du movement des fluides élastiques, que, de quelque façon que l’ébranlement s’étende ou se subdivise, la somme totale des forces vives reste constante. Et voilà principalement pourquoi la force vive doit être considérée comme la mesure de la lumière, dont la quantité totale reste toujours à trés peu près la meme, tant qu’elle ne traverse due moins que des millieux très transparens. Les corps noirs et même les surfaces métalliques les plus brillantes ne réflechissent pas à beaucoup près la totalité de la lumière qui tombe sur leur surface; les corps imparfaitement transparens, et même les plus diaphanes, quand ils sont assez épais, absorbent aussi (pour me servir de l’expression usitée) une quantité notable de la lumière incidente; mais il n’en faut pas conclure que le principe de las conservation des forces vives, n’est plus applicable à ces phénomènes; il résulte au contraire de l’idée la plus probable qu’on puisse se faire sur la constitution mécanique des corps, que la somme des forces vives doit toujours rester la même (tant que les forces accélératrices qui tendent à ramener les molécules à leurs positions d’équilibre n’ont pas change d’intensité), et que la quantité de forces vives qui disparaît comme lumière est reproduite en chaleur.”
Should you consider the contents of this letter suitable for the pages of the Philosophical Magazine, I should feel honoured by its publication in that journal.
Giessen, August 14, 1864.
J. C. Bohn, ‘Historic Notes on the Conservation of Energy’, Phil. Mag., 28 (1864), pp. 311–4.
Johann Bohn: Johann Conrad Bohn (1831–97), a German physicist. From 1858 Bohn held a private lectureship at the Physics Institute of the University of Munich having received his doctorate for his historical treatise on the conservation of force. In 1860 he moved to the University of Giessen as associate professor of mathematics and physics. He translated Tyndall’s Heat as a Mode of Motion into German but letters in 1866 show that Tyndall refused him permission to publish. In 1866 he became a professor in Aschaffenburg at the Centralforstlehranstalt (School of Forestry) for the Kingdom of Bavaria, where he taught mathematics and physics and later geodesy until his death in 1897 (CDSB).
The following footnote appeared here in the original: ‘* Phil. Mag. S. 4. Vol. xxviii. P. 25’ (see letter 2098, n. 6).
Descartes: René Descartes (1596–1650), a French philosopher and mathematician, known primarily for his publication of Discourse on Method (1637) and his work on analytical geometry. He is widely held as the one of the founders of seventeenth-century continental rationalism (CDSB).
the following: Bohn here assumed that Tyndall could read Latin.
The following footnote appeared here in the original: ‘† Phil. Mag. S. 3. Vol. xxiii. P. 442 (1843): Mr. Joule, “That the grand agents of nature are by the Creator’s fiat indestructible”’.
Colding: Ludwig August Colding (1815–88), a Danish civil engineer and physicist, who articulated the principle of conservation of energy contemporaneously with, and independently of, James Joule and Julius Mayer (CDSB).
Leibnitz: Gottfried Wilhelm Leibniz (1646–1716), a German polymath and philosopher most noted for his independent development of integral and differential calculus (CDSB).
vis viva: see letter 1981, n. 2.
On the Conservation of Force: H. Helmholtz, ‘The Conservation of Force: A Physical Memoir’ [1847], in R. Kahl (ed), Selected Writings of Hermann von Helmholtz (Middletown, CT: Wesleyan University Press, 1871), pp. 3–55. This work was translated into English in 1863 by Edmund Atkinson.
John Bernoulli: Johann Bernoulli (1667–1748), a Swiss mathematician known for his work on infinitesimal calculus (HLS).
Fresnel: Augustin-Jean Fresnel.
French translation of Thomson’s ‘Chemistry’: T. Thomson, Systèm de Chimie: Supplément (Paris, Chez Méquignon-Marvis, 1822), pp. 536–9.
Please cite as “Tyndall2129,” in Ɛpsilon: The John Tyndall Collection accessed on