Part 36

Footnote 29:

Those that we need are the expansive force acquired by solids and liquids by a given increase of temperature, and the quantity of heat absorbed or relinquished in the changes of volume of these bodies.

Footnote 30:

The recent experiments of M. Oerstedt on the compressibility of water have shown that, for a pressure of five atmospheres, the temperature of this liquid exhibits no appreciable change. (See Annales de Chimie et de Physique, Feb. 1823, p. 192.)

Footnote 31:

Note G, Appendix B.

Footnote 32:

We find in the work called De la Richesse Minérale, by M. Heron de Villefosse, vol. iii. p. 50 and following, a good description of the steam-engines actually in use in mining. In England the steam-engine has been very fully discussed in the Encyclopedia Britannica. Some of the data here employed are drawn from the latter work.

Footnote 33:

Note I, Appendix B.

Footnote 34:

From Transactions of the Edinburgh Royal Society, xiv. 1849; Annales de Chimie, xxxv. 1852.

Footnote 35:

Published in 1824, in a work entitled “Réflexions sur la Puissance Motrice du Feu, et sur les Machines Propres à Developer cette Puissance. Par S. Carnot.” [Note of Nov. 5, 1881. The original work has now been republished, with a biographical notice, Paris, 1878.]

Footnote 36:

An account of the first part of a series of researches undertaken by Mons. Regnault, by order of the late French Government, for ascertaining the various physical data of importance in the theory of the steam-engine, has been recently published (under the title “Relation des Expériences,” etc.) in the Mémoires de l’Institut, of which it constitutes the twenty-first volume (1847). The second part of these researches has not yet been published. [Note of Nov. 5, 1881. The continuation of these researches has now been published; thus we have for the whole series, vol. i. in 1847; vol. ii. in 1862; and vol. iii. in 1870.]

Footnote 37:

Carnot, p. 67.

Footnote 38:

The evolution of heat in a fixed conductor, through which a galvanic current is sent from any source whatever, has long been known to the scientific world; but it was pointed out by Mr. Joule that we cannot infer from any previously-published experimental researches, the actual generation of heat when the current originates in electro-magnetic induction; since the question occurs, is the heat which is evolved in one part of the closed conductor merely transferred from those parts which are subject to the inducing influence? Mr. Joule, after a most careful experimental investigation with reference to this question, finds that it must be answered in the negative. (See a paper “On the Calorific Effects of Magneto-Electricity, and on the Mechanical Value of Heat; by J. P. Joule, Esq.” Read before the British Association at Cork in 1843, and subsequently communicated by the Author to the Philosophical Magazine, vol. xxiii., pp. 263, 347, 435.)

Before we can finally conclude that heat is absolutely generated in such operations, it would be necessary to prove that the inducing magnet does not become lower in temperature, and thus compensate for the heat evolved in the conductor. I am not aware that any examination with reference to the truth of this conjecture has been instituted; but, in the case where the inducing body is a pure electro-magnet (without any iron), the experiments actually performed by Mr. Joule render the conclusion probable that the heat evolved in the wire of the electro-magnet is not affected by the inductive action, otherwise than through the reflected influence which increases the strength of its own current.

Footnote 39:

So generally is Carnot’s principle tacitly admitted as an axiom, that its application in this case has never, so far as I am aware, been questioned by practical engineers. (1849).

Footnote 40:

When “thermal agency” is thus spent in conducting heat through a solid, what becomes of the mechanical effect which it might produce? Nothing can be lost in the operations of nature—no energy can be destroyed. What effect, then, is produced in place of the mechanical effect which is lost? A perfect theory of heat imperatively demands an answer to this question; yet no answer can be given in the present state of science. A few years ago, a similar confession must have been made with reference to the mechanical effect lost in a fluid set in motion in the interior of a rigid closed vessel, and allowed to come to rest by its own internal friction; but in this case the foundation of a solution of the difficulty has been actually found in Mr. Joule’s discovery of the generation of heat, by the internal friction of a fluid in motion. Encouraged by this example, we may hope that the very perplexing question in the theory of heat, by which we are at present arrested, will before long be cleared up. [Note of Sept., 1881. The Theory of the Dissipation of Energy completely answers this question and removes the difficulty.]

It might appear that the difficulty would be entirely avoided by abandoning Carnot’s fundamental axiom; a view which is strongly urged by Mr. Joule (at the conclusion of his paper “On the Changes of Temperature produced by the Rarefaction and Condensation of Air.” Phil. Mag., May 1845, vol. xxvi.) If we do so, however, we meet with innumerable other difficulties—insuperable without farther experimental investigation, and an entire reconstruction of the theory of heat from its foundation. It is in reality to experiment that we must look—either for a verification of Carnot’s axiom, and an explanation of the difficulty we have been considering; or for an entirely new basis of the Theory of Heat.

Footnote 41:

For a demonstration, see § 29.