^{page 73 note *} Sections III. and VII. have been added to this paper since it was read.

^{page 73 note †} Vol. XXIII. p. 133.

^{page 74 note *} The form of the correction is very simple, being

always additive. If T be the temperature as read, t the temperature of the air, and a the scale reading of the commencement of the stem of the particular thermometer, the correction is very nearly

Since t and a are usually small numbers, the correction increases nearly as the square of the temperature to be measured.

Fortunately, the precision of this correction is not very important to the result. It chiefly affects the actual temperatures; for it will be more fully seen hereafter, that if the same instrument be used in the dynamical and statical experiments, being exposed in precisely the same way, the measures will be relatively correct, and the deduction of the conductivity will not thereby be sensibly affected.

^{page 76 note *} See, however, note to Art. 70, below.

^{page 77 note *} By an oversight in the first part of this paper (Art. 19, note), it was stated that in this instance the thermometer was dipped in melted lead.

^{page 82 note *} Pyrometrie. Berlin, 1779, p. 185.

^{page 82 note †} Traité de Physique, vol. iv. p. 669.

^{page 82 note ‡} Théorie Analytique de la Chaleur. 1822.

^{page 82 note §} Traité Elémentaire de la Physique. 1836, p. 197.

^{page 82 note ∥} Compare Note to Art. 3 of this paper.

^{page 82 note ¶} By “mean ratio,” I intend to express, that where more than one 3-inch space is included in the Interval specified in the first column, the number which follows is the average decrement throughout that space. Thus, in Case I. the whole interval from II. to III. feet, shows a decrement from 24°·2 to 9°·33, which would result from the mean ratio of 0·787, four times multiplied into itself.

^{page 83 note *} p = A (1 + at)ⁿ, where p is the elasticity, and t the temperature.

^{page 83 note †} log

^{page 83 note ‡} log p = a + ba ^t + cβ^t.

^{page 84 note *} The formula in this case would be,—

The following adaptation of Young's formula also represents the observations in Case I. very approximately.

v = (·433027 + ·09539 x)^−6·65.

^{page 86 note *} Usually stated at from 320° to 330° Cent., 608° to 626° Fahr. Biot, indeed, gives it as only 260°, inferentially derived from his conduction experiments (Traité de Physique, iv. 677); but this is on the supposition of the logarithmic law prevailing. Crichton, junior, gives 606°·5 Fahr. (T. Thomson); Daniell, 612°; Kupffer, 633°. Supposing any of these last numbers to be correct, the inference must be, that in the conduction experiments described in the present paper, the temperature of melting lead did not extend to the outside of the iron crucible when the origin of the co-ordinates has been taken, but must be sought somewhere in the interior. This conclusion is strengthened by some other, though indirect considerations.

^{page 88 note *} The wiping of the bar I believe to have been unnecessary and injurious. It lowered the temperature, and interfered with the distribution of the heat in the bar.

^{page 88 note †} The 1¼ inch bar had a central hole, and others 1·5 inch distant, right and left. The 1 inch bar had only two holes equidistant from the centre of the bar.

^{page 91 note *} By the formula , where v and v‘ are the excesses of temperature corresponding to the times t and t‘. is the mean ordinate to which the result corresponds. The logarithms are tabular.

^{page 95 note *} Since this was written, I have observed that a like diminution of the ratios of cooling from glass and silver up to a certain point, and afterwards an increase, was noticed by Dulong and Petit, in their admirable Memoir on the Law of Cooling, page 102.—Mem. Acad. Sci. Par.

^{page 96 note *} This corresponds nearly to the relative emissive power of glass and polished silver used by Dulong.

^{page 96 note †} For in Case I. the whole heat lost from a point having a given temperature being represented by the number 1·116, that due to Convection is 1, that due to Radiation is ·116. In Case II. the total loss is 1673, whereof 1 is due to Convection, and ·673 to Radiation.

^{page 100 note *} Namely, the Curve of Statical Temperature and the Statical Curve of Cooling, being the two curves shown in the wood-cut of last page.

^{page 101 note *} Namely, area between ordinates y and y‘ = M (y‘ − y) where M the subtangent equals

^{page 105 note *} Dr Matthiesson in his Experiments on the Electric Conductivity of Iron (Phil. Trans., 1863), has found nearly equally wide variations in different specimens.

^{page 105 note †} If the numbers in the first column of each division of the Table be called A, then A × ·888 will express the conductivity in water-measure for the foot, minute, and Cent, degree; and A × 825 gives the numbers in the third column, where the centimetre is substituted for the foot.

^{page 106 note *} Phil. Trans. 1863, p. 380.

^{page 107 note *} I may be allowed to state here generally, that this anomaly would apparently assign a too great conducting power to iron at low temperatures than we can readily admit. [The case of the 1-inch bar might rather lead to an opposite conclusion, but I have less confidence in the observations made on it for very small excesses of temperature] Both the statical curve and the curve of cooling deviate more and more from the logarithmic form as the temperature-excesses diminish.

^{page 108 note *} The melting point of tin seems to be one of the best determined of the higher temperatures. According to Crichton, Senior (of Glasgow), it is 442° Fahr. [T. Thomson]; Kupffer, 446°; Daniell, 441°. On the melting point of lead, see Art. 70.

^{page 109 note *} I ought perhaps to mention the formula which Professor Rankine has applied with success to express the elasticity of steam at all temperatures (Edin. Phil. Journ. 1849, vol. xlvii. p. 28, and Philos. Mag. 1854, vol. viii. p. 530). It is as follows:—

where P is the elasticity of vapour, and τ the temperature reckoned from an absolute zero (− 274° cent). In applying the formula to the temperature of a bar, there can be no natural zero from which the lengths are reckoned along the bar; and therefore the constants, instead of three in number, may be reckoned as four; putting v instead of P in the above formula, and, instead of τ writing x + D, D being some fourth constant. (See article 67.)

^{page 109 note †} This method was used by me in 1852.