^{page 123 note *} See “Proceedings” of that date, or Philosophical Magazine, 1852, where a sufficiently complete account of the investigations and principal results is given.

^{page 123 note †} That is a scale defined without reference to effects experienced by any particular kind of matter. Such a scale, founded on general thermo-dynamic relations of heat and matter, and requiring reference to a particular thermometric substance only for defining the unit or degree, was, so far as I know, first proposed in a communication to the Cambridge Philosophical Society (Proceedings, May 1848, or Philosophical Magazine, October 1848). The particular thermometric assumption there suggested, was that a thermo-dynamic engine working to perfection, according to Carnot's criterion, would give the same work from the same quantity of heat, with its source and refrigerator differing by one degree of temperature in any part of the scale; the fixed points being taken the same as the 0° and 100° of the centigrade scale. A comparison of temperature, according to this assumption, with temperature by the air thermometer, effected by the only data at that time afforded by experiment, namely, Regnault's observations on the pressure and latent heat of saturated steam at temperatures of from 0° to 230° of the air thermometer, showed, as the nature of the assumption required, very wide discrepance, even inconveniently wide between the fixed points of agreement. A more convenient assumption has since been pointed to by Mr Joule's conjecture, that Carnot's function is equal to the mechanical equivalent of the thermal unit divided by the temperature by the air thermometer from its zero of expansion; an assumption which experiments on the thermal effects of air escaping through a porous plug, undertaken by him in conjunction with myself for the purpose of testing it, (Philosophical Magazine, Oct. 1852,) have shown to be not rigorously but very approximately true. More extensive and accurate experiments have given us data for a closer test (Phil. Trans., June 1853), and in a joint communication by Mr Joule and myself to the Royal Society of London, to be made during the present session, we propose that the numerical measure of temperature shall be not founded on the expansion of air at a particular pressure, but shall be simply the mechanical equivalent of the thermal unit divided by Carnot's function. We deduce from our experimental results, a comparison between differences on the new scale from the temperature of freezing water, and temperatures centigrade of Regnault's standard air thermometer, which shows no greater discrepance than a few hundredths of a degree, at temperatures between the freezing and boiling points, and, through a range of 300° above the freezing point, so close an agreement that it may be considered as perfect for most practical purposes. The form of assumption given below in the text as the foundation of the new thermometric system without explicit reference to Carnot's function, is equivalent to that just stated, inasmuch as the formula for the action of a perfect thermo-dynamic engine, for the investigated in § 25, expresses (§ 42) that the heat used is to the heat rejected in the proportion of the temperature of the source to the temperature of the refrigerator, if Carnot's function have the form there given as a conjecture, and now adopted as the definition of temperature.

^{page 125 note *} On the Changes of Temperature occasioned by the Rarefaction and Condensation of Air. See Proceedings of the Royal Society, June 1844; or, for the paper in full, Phil. Mag., May 1845.

^{page 125 note †} On a Method of discovering experimentally the Relation between the Heat Produced and the Work Spent in the Compression of a Gas. Trans. R.S.E., April 1851.

^{page 137 note *} M. Jules Regnauld has since found experimentally, that 165 copper-hismuth elements balance the electro-motive force of a single cell of Daniell's (See Comptes Rendus, Jan. 9, 1854, or Bibliothéque Univ. de Genève, March 1854), a result agreeing with the estimate quoted in the text, more closely than the uncertainty and indirectness of the data on which that estimate Avas founded would have justified us in expecting. The comparison of course affords no test of the thermo-electric theory; and only shows that, as far as the observations of Weber, and others alluded to, render Pouillet's available for determining the absolute electro-motive force of a copper-bismuth element, the absolute electro-motive force of a single cell of Daniell's, obtained by multiplying it by the number found by M. Regnauld, agrees with that which I first gave on the hypothesis of all the chemical action being electrically efficient (Phil. Mag., Dec. 1851), and so confirms this hypothesis.

^{page 138 note *} The value of J now used being 32·2 × 1390 = 44,758, which is the equivalent of the unit of hour in “absolute units” of work. The “absolute unit of force” on which this unit of work is founded, and which is generally used in magnetic and electro-magnetic expressions, is the force which acting on the unit of matter (one grain) during the unit of time (one second), generates a unit of velocity (one foot per second). The “absolute unit of work” is the work done by the absolute unit of force in acting through the unit of space (one foot).

^{page 138 note †} That is, if I denote the algebraic excess of the specific heat of electricity in copper, above the specific heat of electricity in iron, according to the terms more recently introduced.

^{page 138 note ‡} See § 123. below. Instead of 240°, conjectured from Regnault's observation when these details were first published, 280° is now taken as a closer approximation to the neutral point of copper and iron.

^{page 139 note *} See § 122, below.

^{page 139 note †} When the Theory was first communicated to the Royal Society, I stated these conclusions with reference to temperature by the air thermometer, and therefore in terms of Carnot's absolute function of the temperature, not simply as now in terms of absolute temperature. At the same time, I gave as consequences of Mayer's hypothesis, the same statement in terms of air thermometer temperatures, as is now made absolutely. See Proceedings, Dec. 15, 1851; or Philosophical Magazine, June 1852, p. 532.

^{page 140 note *} See Proceedings, R. S. E., Dec. 15, 1851.

^{page 140 note †} Since this was written, I have found that thermo-electric inversions between copper and an alloy of antimony and bismuth, and between silver and the same alloy, precisely analogous to that between copper and iron more recently discovered by M. Becquerel, were discovered as early 1823. by Professor Cumming of Cambridge, shortly after the thermo-electricity of metals was first brought to light by Seebeck. These, with other experiments, leading to important results especially as to the order of metals and metallic compounds in the thermo-electric series, are described in the Cambridge Transactions for 1823, and in Professor Cumming's Treatise on Electro-dynamics.

^{page 141 note *} This is the only part of the theoretical reasoning as first given, which depended on the application of Carnot's principle, and consequently, is the only part capable of being objected to as uncertain. All doubt would be removed by an experimental verification of the stated Peltier effects for copper and iron, at the different temperatures, such as I hope very soon to have completed. In the meantime, instead of the theoretical reasoning, we may, if it is preferred, use an ample foundation of analogy to conclude that heat is absorbed at the hotter junction, and evolved at the colder, by the actual thermo-electric current in every case of a circuit of two metals, with their junctions differing but little in temperature. For it was found by Peltier himself, that currents from bismuth to copper, from copper to antimony, from zinc to iron, from copper to iron, and from platinum to iron, cause absorption, and the reverse current in each case, evolution of heat; experimental conclusions, with which I was not acquainted when I first published the Theory. Very soon after I found, myself, by experiment, that copper and iron at ordinary atmospheric temperatures, exhibit the anticipated thermal phenomenon; and corresponding experimental results have been obtained still more recently in the cases of bismuth and copper, copper and antimony, copper and iron, German silver and iron, by Frankenheim. (Poggendorff's Annalen, Feb. 1854); in every case, the current which would be produced by heating one junction a little, being that which in the same junction causes an absorption of heat. If we consider the induction sufficient to establish this as a universal law in thermo-electricity, the reasoning in the text becomes independent of any hypothesis to which objections can possibly be raised.

^{page 146 note *} See § 140, below.

^{page 148 note *} See Proceedings of that date, or Philosophical Magazine, 1850.

^{page 149 note *} Proceedings R. S. E., Dec. 15, 1851. or extract of Proceedings R. S., May 1854, quoted above, § 124.

^{page 164 note *} Cambridge and Dublin Mathematical Journal.

^{page 167 note *} [Added, Liverpool, Sept., 27, 1854.]—As is perfectly illustrated by M. Foucault's beautiful experiment of a rotating solid, placing its axis parallel to that of the earth's, and so turned that it may itself be rotating in the same direction as the earth; which the meeting of the British Association just concluded has given me an opportunity of witnessing.

^{page 167 note †} [Added, Sept. 13, 1854.]—By an experiment made to test its existence, which has given only negative results, I have ascertained that this “rotatory power” if it exists in inductively magnetized iron at all, must be very small in comparison with the amount by which the thermo-electric power, in the direction of magnetization, differs from the thermo-electric power of the same metal not magnetized.