which are necessarily greatly modified by the form of the
enclosure in a manner which it would appear hopeless to
attempt to represent by any general formula.
28. Surface Emissivity.—The same remark applies to many attempts which have since been made to determine the general value of the constant termed by Fourier and early writers the “exterior conductibility,” but now called the surface emissivity. This coefficient represents the rate of loss of heat from a body per unit area of surface per degree excess of temperature, and includes the effects of radiation, convection and conduction. As already pointed out, the combined effect will be nearly proportional to the excess of temperature in any given case provided that the excess is small, but it is not necessarily proportional to the extent of surface exposed except in the case of pure radiation. The rate of loss by convection and conduction varies greatly with the form of the surface, and, unless the enclosure is very large compared with the cooling body, the effect depends also on the size and form of the enclosure. Heat is necessarily communicated from the cooling body to the layer of gas in contact with it by conduction. If the linear dimensions of the body are small, as in the case of a fine wire, or if it is separated from the enclosure by a thin layer of gas, the rate of loss depends chiefly on conduction. For very fine metallic wires heated by an electric current, W. E. Ayrton and H. Kilgour (Phil. Trans., 1892) showed that the rate of loss is nearly independent of the surface, instead of being directly proportional to it. This should be the case, as Porter has shown (Phil. Mag., March 1895), since the effect depends mainly on conduction. The effects of conduction and radiation may be approximately estimated if the conductivity of the gas and the nature and forms of the surfaces of the body and enclosure are known, but the effect of convection in any case can be determined only by experiment. It has been found that the rate of cooling by a current of air is approximately proportional to the velocity of the current, other things being equal. It is obvious that this should be the case, but the result cannot generally be applied to convection currents. Values which are commonly given for the surface emissivity must therefore be accepted with great reserve. They can be regarded only as approximate, and as applicable only to cases precisely similar to those for which they were experimentally obtained. There cannot be said to be any general law of convection. The loss of heat is not necessarily proportional to the area of the surface, and no general value of the coefficient can be given to suit all cases. The laws of conduction and radiation admit of being more precisely formulated, and their effects predicted, except in so far as they are complicated by convection.
29. Conduction of Heat.—The laws of transference of heat in the interior of a solid body formed one of the earliest subjects of mathematical and experimental treatment in the theory of heat. The law assumed by Fourier was of the simplest possible type, but the mathematical application, except in the simplest cases, was so difficult as to require the development of a new mathematical method. Fourier succeeded in showing how, by his method of analysis, the solution of any given problem with regard to the flow of heat by conduction in any material could be obtained in terms of a physical constant, the thermal conductivity of the material, and that the results obtained by experiment agreed in a qualitative manner with those predicted by his theory. But the experimental determination of the actual values of these constants presented formidable difficulties which were not surmounted till a later date. The experimental methods and difficulties are discussed in a special article on Conduction of Heat. It will suffice here to give a brief historical sketch, including a few of the more important results by way of illustration.
30. Comparison of Conducting Powers.—That the power of transmitting heat by conduction varied widely in different materials was probably known in a general way from prehistoric times. Empirical knowledge of this kind is shown in the construction of many articles for heating, cooking, &c., such as the copper soldering bolt, or the Norwegian cooking-stove. One of the earliest experiments for making an actual comparison of conducting powers was that suggested by Franklin, but carried out by Jan Ingenhousz (Journ. de phys., 1789, 34, pp. 68 and 380). Exactly similar bars of different materials, glass, wood, metal, &c., thinly coated with wax, were fixed in the side of a trough of boiling water so as to project for equal distances through the side of the trough into the external air. The wax coating was observed to melt as the heat travelled along the bars, the distance from the trough to which the wax was melted along each affording an approximate indication of the distribution of temperature. When the temperature of each bar had become stationary the heat which it gained by conduction from the trough must be equal to the heat lost to the surrounding air, and must therefore be approximately proportional to the distance to which the wax had melted along the bar. But the temperature fall per unit length, or the temperature-gradient, in each bar at the point where it emerged from the trough would be inversely proportional to the same distance. For equal temperature-gradients the quantities of heat conducted (or the relative conducting powers of the bars) would therefore be proportional to the squares of the distances to which the wax finally melted on each bar. This was shown by Fourier and Despretz (Ann. chim. phys., 1822, 19, p. 97).
31. Diffusion of Temperature.—It was shown in connexion with this experiment by Sir H. Davy, and the experiment was later popularized by John Tyndall, that the rate at which wax melted along the bar, or the rate of propagation of a given temperature, during the first moments of heating, as distinguished from the melting-distance finally attained, depended on the specific heat as well as the conductivity. Short prisms of iron and bismuth coated with wax were placed on a hot metal plate. The wax was observed to melt first on the bismuth, although its conductivity is less than that of iron. The reason is that its specific heat is less than that of iron in the proportion of 3 to 11. The densities of iron and bismuth being 7.8 and 9.8, the thermal capacities of equal prisms will be in the ratio .86 for iron to .29 for bismuth. If the prisms receive heat at equal rates, the bismuth will reach the temperature of melting wax nearly three times as quickly as the iron. It is often stated on the strength of this experiment that the rate of propagation of a temperature wave, which depends on the ratio of the conductivity to the specific heat per unit volume, is greater in bismuth than in iron (e.g. Preston, Heat, p. 628). This is quite incorrect, because the conductivity of iron is about six times that of bismuth, and the rate of propagation of a temperature wave is therefore twice as great in iron as in bismuth. The experiment in reality is misleading because the rates of reception of heat by the prisms are limited by the very imperfect contact with the hot metal plate, and are not proportional to the respective conductivities. If the iron and bismuth bars are properly faced and soldered to the top of a copper box (in order to ensure good metallic contact, and exclude a non-conducting film of air), and the box is then heated by steam, the rates of reception of heat will be nearly proportional to the conductivities, and the wax will melt nearly twice as fast along the iron as along the bismuth. A bar of lead similarly treated will show a faster rate of propagation than iron, because, although its conductivity is only half that of iron, its specific heat per unit volume is 2.5 times smaller.
32. Bad Conductors. Liquids and Gases.—Count Rumford (1792) compared the conducting powers of substances used in clothing, such as wool and cotton, fur and down, by observing the time which a thermometer took to cool when embedded in a globe filled successively with the different materials. The times of cooling observed for a given range varied from 1300 to 900 seconds for different materials. The low conducting power of such materials is principally due to the presence of air in the interstices, which is prevented from forming convection currents by the presence of the fibrous material. Finely powdered silica is a very bad conductor, but in the compact form of rock crystal it is as good a conductor as some of the metals. According to the kinetic theory of gases, the conductivity of a gas depends on molecular diffusion. Maxwell estimated the conductivity of
