From John Herschel   June 18 1864¹

Collingwood June 18 1864

Dear Sir

I beg to thank you for your papers on “Scientific History—on “Molecular Physics and on “a magnetic experiment.”² They are extremely interesting and the experiments by which they are illustrated must on those who were so fortunate as to witness them have made a great impression.

The beautiful experiment of the change of length of a bar of iron, and the parallel arrangement of iron dust in a liquid bring strongly to my recollection an hypothetical explanation of muscular action by nervous influence (assumed to be Volta-electric) on the pendicules of a muscle which I put forth (vivâ voce,³ on a black board) at one of the meetings of the British Association—either that at Southampton in 1846 or at Leeds (I forget which)⁴ It was to this effect. Conceive a muscular fibre to consist of a string of (very oblate) spheroidal particles enclosed in an inextensible close fitting sheath or envelope—insulated from each other by contractions in the sheath and from the sheath itself by a film of lubricating fluid. Let each of these spheroids be, or be capable of becoming, under electric influence, a magnet having its axis of polarity in the direction of the short axis of the spheroid and suffer the whole film to be surrounded with a galvanic spire or spherical thread of nerve conveying an electric current. Thus,

the arrangement A being that of the spheroid unexcited and B that when excited, and their axes arranged pole to pole

by the directive power of the spiral line, the envelope (being perfectly flexible and perfectly lubricated) would be swollen laterally & shortened longitudinally by the rotation through 90° of such enclosed spheroid. The thing is much clearer to conception if we consider the spheroids as mere plane elliptic discs surrounded with a continuous string, inextensible in length, where it is obvious that the rotation of the ellipses within their loops will shorten the interval between the extremities of the system.*

The magnetization of the spheroids might be conceived by regarding them each as a spiral coil, fed by a minute nervous filament long and loose enough (in the lubricating fluid) not to be broken by the rotation of the spheroids.

As this was explained incidentally in some discussion that arose on a paper read I do not think it found its way into any printed volume of proceedings—but I perfectly remember the fact of having so explained it though I cannot call to mind what was the particular subject of discussion.

It is very evident that this implies the converse principle that any cause which may temporarily dispose the longer axes of all the pendicules of a body in some one direction will lengthen the body in that direction just as any which so disposes their shorter, will shorten it. And this is if I apprehend you rightly (in p. 5.) precisely your principle of explanation of the lengthening of your bar.

Being on the subject of these papers I may notice an expression in your note on p. 12 in the “Notes on Scientific History” where you say “all this and much more was stated by Sir J. H. in 1833. &c but Mayer was the first &c &c. Among the “much more” is the broad statement that the source of the great deposit of dynamical efficiency laid up for human use in the coal strata, is the sun: which every body persists in ascribing to Stevenson⁵ who if I mistake not puts it forth (of course independently) at a later date.—and there is, I am told a passage in some poem⁶ published by Effingham Wilson⁷ in 1831 (and which I had no knowledge of) which contains some similar suggestion. The term “vivifying action” is certainly vague but if light & heat be motion and nothing but motion it is difficult not to draw the conclusion that it is in some latent form of heat that the efficiency is stored up. And here I would refer you to a short paper ⁸that I published in the London Ed. and Dublin Phil. Mag. for 1833 iii. p. 401 “On the absorption of light by coloured media” dated Oct 17 of 1833 in which occurs inter alia this expression (I cite from memory not having it by me) “Thus the question “what becomes of Light?” merges in the more general one ‘what becomes of motion, and the answer is ‘it continues for ever” The only further question then, as even yet, unanswered and so far as I see at present unanswerable being as to what portion of that motion in the form of rotary movement may remain confined to individual molecules, and what may continue to subsist in the form of propagated undulation reflected to and fro in the interior of bodies. Whether heat be vis viva seems to me a question whose answer depends very much on the notion people may form of vis viva. To me it conveys absolutely no other meaning than mass x square of velocity and in this sense its amount in a system of moving bodies or molecules is assuredly not a constant quantity. Take only the case of two bodies revolving round their common centre of gravity in elliptic orbit. Their masses are constant—their velocities variable, and variable in the same direction (i.e. both increase together or both decrease) so that the total vis viva mv² + MV² has a maximum & a minimum. If the Vis Viva’s in different states of a system be not the same there must be a difference and this difference is, as is shewn in Mcc. Col. I. v. § 19. a function of the coordinates of the molecules (i.e. ultimately of their mutual distances)—To this difference if any one chuse to give the name “Potential vis viva” it then becomes a truism to say that the sum of the actual and the potential V. V. is invariable. If it be then said that this “ Potential” expresses the attractive force expended in bringing the molecules from the one situation to the other—this again is mere assertion or equally reducible to a truism (if true) by a mere algebraic manipulation such as would insulate on one side of an equation the attractive force supposed to be “expended” and bring the masses, velocities, &c on the other: the fact being that refuge is here taken in the metaphysical conception of “Force” ie effort & its mode of supply & expenditure about which we know nothing and may assert anything.

I ought to apologize for running out into such a digression but the fact is that I cannot reconcile myself to the exceeding laxity of language into which I observe a tendency among physicists at present to fall—in confounding the terms force, motion, energy, meaning sometimes mechanical effort, sometimes vis viva, and sometimes actually mere momentum among whom heat, light, electricity, are often spoken of as forces &c &c. I think we owe much of this confusion to Groves title of his book “The Correlation of Physical Forces” and to the “Forces of nature” so often spoken of by Humboldt in his Kosmos.⁹

Your results about radiant heat and diathermancy are excessively interesting and open an immense field of more important results

There is a very curious consequence which would follow from the admission as a general & rigorous proposition that all expenditure of mechanical force which produced no other perceptible result, produces heat.—The precession of the equinoxes ought to heat the earth. For that movement which we call precession is the result of the Sun & Moon’s mechanical force and consists in a conical motion of the Earth’s axis of rotation.—Let the Earth stand with a given position of its axis. After 26000 years its axis will be again in the same position—the rotating motion is unaltered, and there is no sensible alteration in any particular cognisable to the senses. - What has become of all this “Energy” that has been expended in this interval?

Once more begging you to excuse these longueurs believe me

Dear Sir | Yours very truly | J. F. W. Herschel

*and that by a force the greater, the nearer the ellipses approach to circles

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