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thus increased fourfold. In no case did this correction exceed 7 per cent. The extreme divergence of the resulting values of the diffusivity, including eight independent series of measurements on difl’erent days, was less than 1 per cent. Observations were taken at mean temperatures of 102“ C. and 54° C., with the following results :— Tablk II. Diffusity of Sandy Soils. C.G.S. Units. Cast-iron at 102“ C., */c=‘1296, c='858, *=‘1113 „ „ 54“ C., kjc— -1392, c= -823, *= T144. Thermo- DiffusSoil. Locality. Observer. The variation of c was determined by a special series of experimeter. ivity. ments. No allowance was made for the variation of density with temperature, or for the variation of the distance between the thermometers, owing to the expansion of the bar. Although this •0087 Kelvin, 1860. Garden sand. Edinburgh. Mercury. correction should be made if the definition were strictly followed, •0136 Neumann, 1863 Sandy loam. it is more convenient in practice to include the small effect ot Greenwich. •0125 Everett, 1860. Gravel. linear expansion in the temperature-coefficient in the case of solid Angstrom, 1861 Sandy clay. Upsala. •0057 bodies. •0045 Coarse sand. •0094 17. Lorentz’s Method.—Neumann, Weber, Lorentz, and others Angstrom have employed similar methods, depending on the observation The same soil, place, and instruments •0061 Rudberg. of the rate of change of temperature at certain points of bars, reduced for different years. •0074 Quetelet. rings, cylinders, cubes, or spheres. Some of these results have Callendar, 1895 Garden sand. Montreal. Platinum. ‘•0036 been widely quoted, but they are far from consistent, and it may •0074 Oxford. Rambaut, 1900 Gravel. be doubted whether the difficulties of observing rapidly varying temperatures have been duly appreciated in many cases. From The low value at Montreal is chiefly due to the absence an experimental point of view the most ingenious and complete of percolation during the winter. Itambaut’s results were method was that of Lorentz (Wied. Ann. xiii. p. 422, 1881). He the variations of the mean temperature of a section of a obtained with similar instruments similarly located, but deduced bar from the sum S of the E.M.F’s. of a number of couples, he did not investigate the seasonal variations of diffusivity, inserted at suitable equal intervals l and connected in series. The or the effect of percolation. It is probable that the coarser difference of the temperature gradients D/7 at the ends of the soils, permitting more rapid percolation, would generally section was simultaneously obtained from the difference D of readings of a pair of couples at either end connected in give higher results. In any case, it is evident that the the opposition. The external heat-loss was eliminated by comparing transmission of heat by percolation would be much greater observations taken at the same mean temperatures during heating in porous soils and in the upper layers of the earth’s crust and during cooling, assuming that the rate of loss of heat f{S) than in the lower strata or in solid rocks. It is probable would be the same in the two cases. Lorentz thus obtained the for this reason that the average conductivity of the earth’s equations— Heating, qk D/l = cqldS/dt+f(S). crust, as deduced from surface observations, is too large; Cooling, qk D'/l = cql dS'/dt'+f(S'). and that estimates of the age of the earth based on such Whence k — cP(dS/dt - dS'/dt')J(I) - D'). (7) measurements are too low, and require to be raised; they It may be questioned whether this assumption was justifiable, would thereby be brought into better agreement with the since the rate of change and the distribution of temperature were conclusions of geologists derived from other lines of quite different in the two cases, in addition to the sign of the change itself. The chief difficulty, as usual, was the determinargument. ation of the gradient, which depended on a difference of potential 16. Angstrom’s Method consists in observing the propagation of of the order of 20 microvolts between two junctions inserted in heat waves in a bar, and is probably the most accurate method small holes 2 cms. apart in a bar 1‘5 cms. in diameter. It was for measuring the diffusivity of a metal, since the conditions may also tacitly assumed that the thermo-electric power of the couples be widely varied and the correction for external loss of heat can for the gradient was the same as that of the couples for the mean be made comparatively small. Owing, however, to the laborious temperature, although the temperatures were different. This nature of the observations and reductions, the method does not might give rise to constant errors in the results. Owing to the appear to have been seriously applied since its first invention, difficulty of measuring the gradient, the order of divergence of except in one solitary instance by the writer to the case of cast-iron individual observations averaged 2 or 3 per cent., but occasionally (Fig. 1). The equation of the method is the same as that for reached 5 or 10 per cent. The thermal conductivity was determined the linear flow with the addition of a small term representing in the neighbourhood of 20“ C. with a water jacket, and near 110 the radiation loss. The mathematical solution is given in the C. by the use of a steam jacket. The conductivity of the same bars article Heat (Ency. Brit. vol. xi.), assuming that k and c are was independently determined by the method of Forbes, employing both constants, and the coefficient of cooling also constant, over an ingenious formula for the heat-loss in place of Newtons law. the range of the experiment. This is an admissible approxima- The results of this method differ 2 or 3 per cent, (in one case nearly tion if the range is small. The apparatus of Fig. 1 was designed 15 per cent.) from the preceding, but it is probably less accurate. for this method, and may serve to illustrate it. The steam pressure The thermal capacity and electrical conductivity were measured at in the heater may be periodically varied by the gauge in such a various temperatures on the same specimens oi metal. Owing to manner as to produce an approximately simple harmonic oscilla- the completeness of the recorded data, and the great experimental tion of temperature at the hot end, while the cool end is kept at skill with which the research was conducted, the results are proba steady temperature. The amplitudes and phases of the temper- ably among the most valuable hitherto available. One important ature waves at different points are observed by taking readings result, which might be regarded as established by this work, was of the thermometers at regular intervals. In using mercury that the ratio */*' of the thermal to the electrical conductivity, thermometers, it is best, as in the apparatus figured, to work though nearly constant for the good conductors at any one temperon a large scaleo (4-inch bar) with waves of slow period, about 1 ature such as 0° C., increased with rise of temperature nearly in to 2 hours. Angstrom endeavoured to find the variation of proportion to the absolute temperature. The value found for conductivity by this method, but he assumed c to be the same this ratio at 0“ 0. approximated to 1500 C.G.S. for the best for two different bars, and made no allowance for its variation conductors, but increased to 1800 or 2000 for bad conductors like with temperature. He thus found nearly the same rate of vari- German silver and antimony. It is clear, however, that, this ation for the thermal as for the electric conductivity. His final relation cannot be generally true, for the cast-iron mentioned results for copper and iron were as follows :— in the last section had a specific resistance of 112,000 C.G.S. at 100“ C., which would make the ratio kjk' —12,500. The increase Copper, & = 0-982 (1 -0'00152 0) assuming c= ■84476. of resistance with temperature was also very small, so that the Iron, *=0-1988 (1-0-00287 (?) „ c=-88620. ratio varied very little with temperature. Angstrom’s value for iron, when corrected for obvious numerical errors, and for the probable variation of c, becomes— 18. Electrical Methods.—There are two electrical methods which have been recently applied to the measurement Iron, *=0T64 (1-0-0013 9), of the conductivity of metals, (a) the resistance method, but this is very doubtful as c was not measured. The experiments on cast-iron with the apparatus of Fig. 1 were devised by the writer, and applied by him, and also by varied by taking three different periods, 60, 90, and 120 minutes, King and Duncan, (V) the thermo-electric method, devised and two distances, 6 inches and 12 inches, between the thermometers compared. In some experiments the bar was lagged with by Kohlrausch, and applied by Jaeger and Dieselhorst. 1 inch of asbestos, but in others it was bare, the heat-loss being Both methods depend on the observation of the steady S. HI. — 25

the actual degree of wetness of each may vary considerably. The following are a few typical values for sand or gravel deduced from the annual wave in different localities:—