^{page 133 note *} Report for 1852 (Belfast), p. 260.

^{page 133 note †} Vol. i. p. 5 (1833).

^{page 133 note ‡} This is usually called the Newtonian Law, though it may be doubted how far Newton understood it to apply to internal conduction. (See Phil. Trans. 1701, and Opuscula, tom. ii. p. 419.)

^{page 134 note *} The fallacy of the method of minimum squares, as it is often applied to physical inquiries, is well exemplified in this experiment, and may be seen almost at a glance by inspecting Biot's comparative tables of calculated and observed temperatures, given in his Traité de Physique, vol. iv., p. 666. The “probable error” of an observation of temperature at each and every point of the bar is considered as the same; whereas, when the excesses of temperature are only a few degrees, every experimenter knows that they may be determined with the nicest accuracy, whilst, when the excesses rise to hundreds of degrees, the uncertainty is incomparably greater. It is quite evident, that Biot'S observations differ systematically from the logarithmic law. In referring in 1856 to these observations [Encyclopædia Britannica, Sixth Dissertation, Art. (671)], I observed, that “instead of drawing from them, as he does, an argument for the accuracy of the Newtonian law of cooling, the diminution of temperature along the bar is far more rapid at first, and less afterwards, than that law indicates. In fact, the apparent agreement of the formula is owing to the use, in a case to which it does not correctly apply, of that often misapplied rule of the doctrine of chances—the method of least squares.” See also MrAiry's, Theory of Errors of Observations (1861).Google Scholar

^{page 134 note †} Report for 1851 (Ipswich). Sections, p. 7.

^{page 139 note *} This precaution was a source of considerable trouble to Mr Despretz. See Ann. de Chimie, torn. xix.

^{page 139 note †} The first thermometer of the series along the bar has to be incessantly watched for this purpose, or, better still, a thermometer with the bulb dipped into the lead in the crucible, kept as near the melting point as possible. So dextrous did my assistant at last become, that for hours this last thermometer was prevented from wavering, even at that high temperature, above a very few degrees of Fahrenheit.

^{page 140 note *} It was found that when mercury was used for these last, the surface became hotter by convection than the central part of the hole, contrary to the law of the distribution of heat in a solid bar, and consequently an undue (though perhaps hardly sensible) amount of heat was thereby dissipated. I may add, that I ascertained by actual experiment, that the boring of several additional holes between the extreme holes of a bar did not sensibly disturb the conduction of heat when the intermediate holes had thermometers surrounded by mercury inserted in them.

^{page 142 note *} This interpretation of the physical origin of the periodic functions in the cooling of bodies was given in the Encyclopædia Britannica, Sixth Dissertation, Art. (674). When the circular functions have exhausted themselves, the exponential portion of the expression for the temperature alone remains. See Fourier, , Théorie Analytique de la Chaleur.CrossRefGoogle Scholar

^{page 142 note †} “When coated with paper, the paper begins to singe at a temperature slightly above that of melting tin, or 442° Fahr.

^{page 144 note *} The diagrams referred to in this memorandum are all drawn out, but are not engraved pending the revision of the scales of the thermometers.

^{page 144 note †} K expresses the absolute conducting power in terms of the thermal capacity of water.

^{page 145 note *} Or (more fully) it expresses in centigrade degrees the temperature communicated to a cubic foot of water in one minute, across a plate of iron one foot thick, whose surfaces are maintained at a constant difference of temperature of one degree centigrade.

^{page 145 note †} This is perhaps the most convenient unit of conductivity for general use. The original thermal unit of Fourier (who first gave a correct definition of this quantity) was referred to the minute and the metre as the units of time and length, to the interval from the freezing to the boiling point of water as the unit of temperature and the unit of heat was the quantity required to melt one kilogramme of ice (Théorie, Arts. 68, 69). It is plain from Art. 59, and others of the same work, that Fourier had no idea that the conductivity varied with the actual temperature—an admission which must be held to leave the Newtonian law true in form only, since the flux is proportional in any one substance not to only, but is also a direct function of v.