Hugh Longbourne Callendar

“ Similarly if A is hotter than B, or if there is a gradient of temperature between adjacent layers, the diffusion of molecules from A to B tends to equalize the temperatures, or to conduct heat through the gas at a rate proportional to the temperature gradient, and depending also on the rate of interchange of molecules in the same way as the viscosity effect. Conductivity and viscosity in a gas should vary in a similar manner since each depends on diffusion in a similar way. The mechanism is the same, but in one case we have diffusion of momentum, in the other case diffusion of heat. ”

“ If the flow is steady, and the temperature of each point of the body invariable, the rate of transmission must be everywhere the same. If the gradient is not uniform, its value may be denoted by dθ/dx. In the steady state, the product kdθ/dx must be constant, or the gradient must vary inversely as the conductivity, if the latter is a function of θ or x. One of the simplest illustrations of the rectilinear flow of heat is the steady outflow through the upper strata of the earth’s crust, which may be considered practically plane in this connexion. ”

“ In any case, it is evident that the transmission of heat by percolation would be much greater in porous soils and in the upper layers of the earth’s crust than in the lower strata or in solid rocks. It is probable for this reason that the average conductivity of the earth’s crust, as deduced from surface observations, is too large; and that estimates of the age of the earth based on such measurements are too low, and require to be raised ”

“ The disadvantage is that the thermo-electric force is very small, about ten-millionths of a volt per degree, so that a small accidental disturbance may produce a serious error with a difference of temperature of only 1° between the junctions. The chief uncertainty in applying this method appears to have arisen from variations of temperature at different parts of the surface, due to inequalities in the heating or cooling effect of the stream of water flowing over the surfaces. Uniformity of temperature could only be secured by using a high velocity of flow, or violent stirring. ”

“ At higher pressures the effect of conduction was masked by convection currents. The question of the variation of conductivity with temperature is more difficult. If the effects depended merely on the velocity of translation of the molecules, both conductivity and viscosity should increase directly as the square root of the absolute temperature ”

“ The area A from which the heat is collected need not be the whole surface of the plate, but a measured central area where the flow is most nearly uniform. This variety is known as the “Guard-Ring” method, but it is generally rather difficult to determine the effective area of the ring. There is little difficulty in measuring the time of flow, provided that it is not too short. The measurement of the temperature gradient in the plate generally presents the greatest difficulties. ”

“ The steam pressure in the heater may be periodically varied by the gauge in such a manner as to produce an approximately simple harmonic oscillation of temperature at the hot end, while the cool end is kept at a steady temperature. ”

“ A Simple-Harmonic or Sine Wave is the only kind which is propagated without change of form. In treating mathematically the propagation of other kinds of waves, it is necessary to analyse them into their simple-harmonic components, which may be treated as being propagated independently. ”

“ Faster-moving particles diffusing from A to B carry their momentum with them, and tend to accelerate B; an equal number of slower particles diffusing from B to A act as a drag on A. This action and reaction between layers in relative motion is equivalent to a frictional stress tending to equalize the velocities of adjacent layers. ”

“ A strictly periodic oscillation of this kind occurs in the working of a steam engine, in which the walls of the cylinder are exposed to regular fluctuations of temperature with the admission and release of steam. The curves in fig. 5 are drawn for a particular case, but they apply equally to the propagation of a simple-harmonic wave of any period in any substance changing only the scale on which they are drawn. The dotted boundary curves have the equation θ =±e−mx, and show the rate of diminution of the amplitude of the temperature oscillation with depth in the metal. ”

“ If the plate is thin, it is necessary to measure the thickness with great care, and it is necessary to assume that the temperatures of the surfaces are the same as those of the media with which they are in contact, since there is no room to insert thermometers in the plate itself. ”

“ This gives an average value of the conductivity over the range, but it is better to observe the temperatures at three distances, and to assume k to be a linear function of the temperature, in which case the solution of the equation is still very simple, namely,
where e is the temperature-coefficient of the conductivity. The chief difficulty in this method lay in determining the effective distances of the bulbs of the thermometers from the axis of the cylinder, and in ensuring uniformity of flow of heat along different radii. ”

“ For the particular soil in question it was found that the diffusivity varied enormously with the degree of moisture, falling as low as .0010 C.G.S. in the winter for the surface layers, which became extremely dry under the protection of the frozen ice and snow from December to March, but rising to an average of .0060 to .0070 in the spring and autumn. The greater part of the diffusion of heat was certainly due to the percolation of water. ”

“ The last error is best avoided by employing platinum thermometers buried horizontally. In any case results deduced from the annual wave must be expected to vary in different years according to the distribution of the rainfall, as the values represent averages depending chiefly on the diffusion of heat by percolating water. ”

“ Cylinder Method.—A variation of the tube method, which can be applied to metals and good conductors, depends on the employment of a thick cylinder with a small axial hole in place of a thin tube. The actual temperature of the metal itself can then be observed by inserting thermometers or thermo-couples at measured distances from the centre. This method has been applied by H. L. Callendar and J. T. Nicolson (Brit. Assoc. Report, 1897) to cylinders of cast-iron and mild steel, 5 in. in diam. ”