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 CONDUCTION

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fundamental assumption that the rate of cooling is the same at the linear flow by the projecting bulb of the calorimeter. This the same temperature under the very different conditions existing may partly account for the discrepancy in the following results:— in the two parts of the experiment. They are also partly caused Mercury, £=0'02015 C.G.S. Berget. by the large uncertainties of the corrections, especially those of ,, ‘Weber. the mercury thermometers under the peculiar conditions of the ,, ,, Angstrom. experiment. The results of Forbes are interesting historically as having been the first approximately correct determinations 12. Variable-Firm Methods.—In these methods the of conductivity in absolute value. The same method was applied flow of heat is deduced from observations of the rate by R. W. Stewart {Phil. Trans., 1892), with the substitution of change of temperature with time in a body exposed of thermo-couples (following Wiedemann) for mercury thermometers. This avoids the very uncertain correction for stem- to known external or boundary conditions. No caloriexposure, but it is doubtful how far an insulated couple, inserted metric observations are required, but the results are in a hole in the bar, may be trusted to attain the true tem- obtained in terms of the thermal capacity of unit volume perature. The other uncertainties of the method remain. R. W. Stewart found for pure iron, k— -175 (1 - •0015 t) C.G.S. c, and the measurements give the difFusivity hc, instead Hall using a similar method found for cast-iron at 50° C. the of the calorimetric conductivity It. Since both It and c value UOS, but considers the method very uncertain as ordinarily are generally variable with the temperature, and the mode practised. of variation of either is often unknown, the results of 10. Calorimetric Bar Method.—To avoid the uncertainties of surface loss of heat, it is necessary to reduce it to the rank of these methods are generally less certain with regard to a small correction by employing a large bar and protecting it the actual flow of heat. As in the case of steady-flow from loss of heat. The heat transmitted should be measured methods, by far the simplest example to consider is that calorimetrically, and not in terms of the uncertain emissivity. of the linear flow of heat in an infinite solid, which is The apparatus shown in Fig. 1 was constructed by Callendar and most nearly realized in nature in the propagation of temperature waves in the surface of the soil. One of the best methods of studying the flow of heat in this case is to draw a series of curves showing the variations of temperature with depth in the soil for a series of consecutive days. The curves given in Fig. 2 were ob-
 * =0-01479 ,,
 * =0-0177

Nicolson with this object. The bar was a special sample of castiron, the conductivity of which was required for some experiments on the condensation of steam {Froc. Inst. C.E., 1898). It had a diameter of 4 inches, and a length of 4 feet between the heater and the calorimeter. The emissivity was reduced to one quarter by lagging the bar like a steam-pipe to a thickness of 1 inch. The heating vessel could be maintained at a steady temperature by high-pressure steam. The other end was maintained at a temperature near that of the air by a steady stream of water flowing through a well-lagged vessel surrounding the bar. The heat transmitted was measured by observing the difference of temperature between the inflow and the outflow, and the weight of water which passed in a given time. The gradient near the entrance to the calorimeter was deduced from observations with five thermometers at suitable intervals along the bar. The results obtained by this method at a temperature of 40° C., varied from •116 to ‘IIS C.G.S. from observations on different days, and were probably more accurate than those obtained by the cylinder method. The same apparatus was employed in another series of experiments by Angstrom’s method described below. 11. Guard-Ring Method.—This may be regarded as a variety of the plate method, but is more particularly applicable to good conductors, which require the use of a thick plate, so that the temperature of the metal may be observed at different points inside it. Berget (Journ. Phys. vii. p. 503, 1888) has applied this method directly to mercury, and has determined the conductivity of some other metals by comparison with mercury. In the case of mercury he employed a column in a glass tube 13 mm. in diam. surrounded by a guard cylinder of the same height, but 6 to 12 cm. in diam. The mean section of the inner column was carefully determined by weighing, and found to be I'lOS sq. cm. The top of the mercury was heated by steam, the lower end rested on an iron plate cooled by ice. The temperature at different heights was measured by iron wires forming thermojunctions with the mercury in the inner tube. The heat-flow through the central column amounted to about 7'5 calories in 54 seconds, and was measured by continuing the tube through the iron plate into the bulb of a Bunsen ice calorimeter, and observing with a chronometer to a fifth of a second the time taken by the mercury to contract through a given number of divisions. The calorimeter tube was calibrated by a thread of mercury weighing 19 milligrams, which occupied eighty-five divisions. The contraction corresponding to the melting of 1 gramme of ice was assumed to be •0906 c.c., and was taken as being equivalent to 79 calories (1 calorie = 15 •59 mgrm. Hg.). The chief uncertainty of this method is the area from which the heat is collected, which probably exceeds that of the central column, owing to the disturbance of

Fig. 2. tained from the readings of a number of platinum thermometers buried in undisturbed soil in horizontal positions at M‘Gill College, Montreal. The method of deducing the difFusivity from these curves is as follows :— The total quantity of heat absorbed by the soil per unit area of surface between any two dates, and any two depths, af and x", is equal to c times the area included between the corresponding curves. This can be measured graphically without any knowledge of the law of variation of the surface temperature, or of the laws of propagation of heat waves. The quantity of heat absorbed by the stratum (a;' a;") in the interval considered can also be expressed in terms of the calorimetric conductivity *. The heat transmitted through the plane x is equal per unit area of surface to the product of * by the mean temperature gradient (dd/dx) and the interval of time, T- T'. The mean temperature gradient is found by plotting the curves for each day from the daily observations. The heat absorbed is the difference of the quantities transmitted through the bounding planes of the stratum. We thus obtain the simple equation— lcdQ'Jdx!)- Id'tdQ"jdx")—c (area between curves)/^- T'), (4) by means of which the average value of the difFusivity */c can be found for any convenient interval of time, at different seasons of the year, in different states of the soil. 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. On some occasions, owing to the sudden melt-