Page:Encyclopædia Britannica, Ninth Edition, v. 11.djvu/612

Rh 578 HEAT ture of 1 4 C., while the other had the varying tempera ture of the centre of the ball. Two sets of experiments were made. In one the ball had a brighb surface, in the other it was coated with soot from the flame of a lamp, and in both the air was kept moist by a saucer of water placed in the interior of the tinplate enclosure. The re sults are given in terms of the number of units of heat lost per second, per square centimetre of surface of the copper, per degree of difference between the temperatures of the two junctions. 72. Returning to the conduction of heat, we have first to say that the theory of it was discovered by Fourier and given to the world through the French Academy in his Tkyorie Analytique de la Chaleur, 1 with solutions of pro blems naturally arising from it, of which it is difficult to say whether their uniquely original quality, or their transcend- enfcly intense mathematical interest, or their perennially im portant instructiveness for physical science, is most to be praised. Here we can but give the very slightest sketch of the elementary law of conduction in an isotropic substance, the mathematical expression for it in terms of orthogonal plane or curved coordinates, and a few of the elementary solutions in Fourier s theory. 73. Consider a slab of homogeneous solid bounded by two parallel planes. Let the substance be kept at two dif ferent temperatures over these parallel planes by suitable sources of heat and cold. For example, let one side be kept cold by a stream of cold water, or by a large quantity of ice and water in contact with it, and the other kept warm by a large quantity of warm water or by steam blown against it. Whatever particular plans of heater and refri gerator be adopted, care must be taken that the temperature be kept uniform over the whole, or over a sufficiently large area of each side of the slab, to render the isothermal surfaces sensibly parallel planes through the whole of the slab intercepted between the two calorimetric areas, and that the temperature at each side is prevented from varying with time. It will be found that heat must con tinually be applied at one side and removed from the other, to keep the circumstances in the constant condition thus defined. When this constant condition of surface tempera ture is maintained long enough, the temperature at every point of the slab settles towards a constant limiting value ; and when this limiting value has been sensibly reached by every point of the slab, the temperature throughout remains sensibly constant so long as the surface temperatures are kept constant. In this condition of affairs the temperature varies continuously from one side of the slab to the other ; and it is constant throughout each interior plane parallel to the sides ; in other words, the isothermal surfaces are paral lel planes. Let V and V be the temperatures in two of these isothermals and a the distance between them. The V V quotient is the average rate of variation of tem perature per unit of length between these two isothermals. Let Q be the quantity of heat taken in per unit of time at a certain area A on one side, and emitted at the correspond ing area of the other side of the slab, measured by proper calorimetrical appliances to these areas, which we shall call the calorimetric areas of the apparatus. It will generally be found that the value of the quotient (V - V )/a is not the same for consecutive isothermal surfaces. For metals it is ascertained by experiment that it increases continuously from the cold side to the hot side of the slab. In other words, as we shall see presently, the thermal conductivity of the substance is not generally the same at different temperatures, and for metals it is smaller the higher the temperature. 1 A translation into English by Freeman has been recently published, in 1 vol. 8vo, by the Cambridge University Press, 1879. 74. Circumstances being as described in 73, the thermal conductivity of the substance between the isother mals v and v is the value of It must be remembered that the temperatures v, v used in this definition are temperatures of the substance itself. Some experimenters have given largely erroneous results through assuming that the temperatures of the two sides of the slab were equal to those of the calorimetric fluids, such water, with its temperature measured by a thermometer, on the other side. To obtain correct results, the actual tem peratures at two points in the conducting body itself must be ascertained by aid of suitable thermometers, or thermo meters and differential thermoscopes, applied in such a way as not sensibly to disturb the isothermal surfaces. This, far as we know, has not been done by any experimenter hitherto in attempting to measure thermal conductivity directly by the method indicated in the definition ; and therefore if any results obtained by this method hitherto are trustworthy, it is only in a few cases, cases in which, un less the substance experimented upon has been of such small conducting power, and the stirring of the calorimetric fluids on its two sides so energetic, that we can feel sure that the observed or assumed temperatures of these fluids, or of the portions of them of which the temperatures have been measured by thermometers, have not differed sensibly from the temperatures of the slab at its surfaces in contact ! with them. 75. What utter confusion has permeated scientific literature, from experiments on thermal conductivity vitiated through non-fulfilment of this condition, is illustrated by results quoted in Everett s Units and Physical Constants (London, 1879), among which we find 19 for the conduc tivity of copper according to Pticlet, and I l according to ! Angstrom (which we now know to be correct). When we 1 look to Peclet s and Angstrom s own papers the confusion ! becomes aggravated. Pdclet, in his Memoire sitr la deter mination des coefficients de conductibilite des metanx par la chaleur, 2 qiiotes old experiments of Cle ment, and others more recent of Thomas and Laurent, regarding which he gives certain details. Taking his information no doubt from Pdclet s paper, Angstrom gives a statement 3 for the conductivity of copper, according to experimenters who had preceded him, which, with the decimal point shifted two places to the left to reduce to C. G. S., is as follows : Clement, 00231 Thomas and Laurent, 0122 Pcclet, 178 But Angstrom did not notice that Pe clet had stated the thickness of the plate experimented on by Cle ment to be between 2 and 3 millimetres. Pe clet himself in his next sentence seems to have forgotten this when he compares the figure &quot;23 which he had calculated from Clement s results, without taking account of the thickness of the plate, with 1 22 which he calculates from Thomas and Laurent s experiments on copper, without stating any thickness for the 1 tube of copper on which (instead of a flat plate) they had their results really were in either Pe clet s or Angstrom s ! paper ; but Pticlet seems to show enough regarding it to let us now feel perfectly sure that it is only a question of 2 Amyzlcs de Chimie et de Physique, Paris, 1841. 3 In Angstrom s own statement the unit quantity of heat is that required to raise 1000 grammes of water 1. The conduction is reckoned per square metre of the copper plate per second of time, and the unit chosen for the rate of variation of temperature across the plate is 1 per millimetre. To reduce his numbers to the C. G. S. system we must therefore multiply by 10 3 x 10~ 4 x 10- 1 = 10- a.
 * as warm water or steam on one side, and iced water or cold
 * -experimented. Thus we have no data for finding what