To James Joule¹

Royal Institution, London

My Dear Joule,

On my return from Switzerland two days ago,² I became acquainted with the note which you have published in the last Number of the Philosophical Magazine.³ Would you allow me to make the following remarks in connexion with the subject of it?

During the spring of the present year I gave at the Royal Institution a course of lectures “On Heat, regarded as a kind of Motion.”⁴ During the early portion of the course, I had engaged a short-hand writer to report the lectures, with a view to their subsequent publication; and from this gentleman’s notes of my second lecture I make the following extract, which refers to the mechanical theory of heat:—“It is to Mr. Joule, of Manchester, that we are almost wholly indebted for the experimental treatment of this subject. With his mind firmly fixed upon a principle, and undismayed by the coolness with which his first labours appear to have been received, he persisted for years in his attempts to prove the invariability of the relation between heat and ordinary mechanical force. He placed water in a suitable vessel, agitated it by paddles moved by measurable forces, and determined the elevation of temperature; he did the same with mercury and sperm-oil. He also caused disks of cast iron to rotate against each other, and measured the heat produced by their friction. He urged water through capillary tubes, and measured the heat thus generated. The results of his experiments leave no doubt upon the mind that under all circumstances the absolute amount of heat produced by the expenditure of a definite amount of mechanical force is fixed and invariable.” Such has been my language regarding you; and to it I still adhere. I trust you find nothing in it which indicates a desire on my part to question your claim to the honour of being the experimental demonstrator of the equivalence of heat and work.

It was not my object in the lecture to which you refer to give a history of the mechanical theory of heat, but simply to place a man of genius, to whom the fates had been singularly unkind, in a position in some measure worthy of him. I was quite aware of all that you have stated regarding Locke,⁵ Rumford,⁶ Davy, and others: you might have added Bacon⁷ to your list. Probably no great generalization was ever established without having first simmered in the minds of many thinkers. But the writings of Mayer form an epoch in the history of this subject; and I certainly should not feel disposed to retract a single sentence that I have written in his favour. I believe he deserves more praise than I have given him. It was he who first used the term “equivalent” in the precise sense in which you have applied it; he calculated the mechanical equivalent of heat from data which, as I have said, “a man of rare ingenuity alone could turn to account;” and his calculation is in striking accordance with your own experimental determinations*. You worked independently of Mayer, and in a totally different way. You brought the mechanical theory to the test of experiment, and in this way proved its truth.

Mayer calculated correctly the mechanical equivalent of heat; but you say that, at the time he wrote, there were no known facts to warrant the hypothesis which he adopted. If by this you mean to say that he made a haphazard guess which had no basis of physical probability, I cannot agree with you. The known constitution of an elastic fluid is, in my opinion, quite sufficient to justify Mayer’s proceeding. His hypothesis was this: – Let the quantity of heat required to raise the temperature of gas, preserved at a constant volume, t°, be x, and let the heat required to raise the same gas, under constant pressure, t°, be x + y. The weight raised by the expanding gas in the latter case being P, and the height to which it is raised h, then, according to Mayer,

y = P x h ;

that is to say, the excess of heat imparted in the latter case is precisely equivalent to the mechanical work performed.

It is undoubtedly implied in this equation that the quantity of heat y is expanded wholly in external work, and that none of it has been consumed in overcoming internal molecular attractions. This, I think, on the face of it is an extremely probable hypothesis – so probable, indeed, as to amount, in my estimation, almost to a certainty. Clausius makes the same assumption with no better authority than Mayer; and I believe (for I here trust my memory merely) that the assumption has been completely verified by the experiments of the very philosophers who once questioned it. “The law,” says Mayer, “‘Heat=Mechanical effect,’ is independent of the nature of an elastic fluid, which only serves as the apparatus by means of which the one force is converted into the other.”

The law of Mariotte⁸ was an old principle when Mayer wrote; and the fact of its holding good for gases generally renders the conclusion exceedingly probable that, in yielding to compression, the attractions of the gaseous molecules were insensible; otherwise it is hardly conceivable that the same results could have been obtained with gases so differently constituted: the attractions of the hydrogen atoms, for example, would in all probability be different from those of oxygen. Mayer was further justified in his hypothesis, as to the absence of interior work in the case of a true gas, by the experiments of (Ersted⁹ and Despretz,¹⁰ which showed that the law of Mariotte was departed from by the liquefiable gases – the amount of departure depending on the proximity of the gas to its point of condensation. Where, therefore, no departure from the law had been observed (in the case of air for instance), Mayer, I submit was perfectly warranted in assuming that the molecular attractions were insensible, and that the quantity of heat (y) before referred to was entirely expended in raising the weight, and had its true mechanical equivalent in the weight so raised.

With reference to the application of the mechanical theory of heat to cosmical phenomena, if it were not a liberty, I would ask whether you have ever read the essay of Mayer entitled Beiträge zur Dynamik des Himmels?¹¹ If so, then I have good reason to suspect my competence to come to a correct conclusion as to what constitutes a scientific right.

Knowing that the original memoirs of Mayer would be the true court of appeal in connexion with this subject, I some months ago urged the responsible editor of the Philosophical Magazine to publish translations of them. This I hope he will do; for I quite agree with you in thinking that they would interest many of the readers of the Magazine. Let me add, in conclusion, that I do not think the public estimate of your labours can be in the least affected by any recognition which may be accorded to Mayer. There is room for both of you on this grand platform. Certainly, had Mayer never written a syllable on the mechanical theory of heat, I should not deem your work a whit nobler than I now hold it to be.

Believe me, | Yours, &c., | John Tyndall | Royal Institution, | August 1862

J. Tyndall, ‘Mayer, and the Mechanical Theory of Heat’, Phil. Mag., 24 (1862), pp. 173–5