XXXVI. Experiments on the Heat-conductivity of Stone, based on Fourier's Théorie de la Chaleur.' By W. E. AYRTON and JOHN PERRY, Professors in the Imperial College of Engineering, Tokio, Japan*.

[Plates IX. and X.]

I. WHEN a body is a good conductor for heat, it is compa

ratively easy to find the conductivity correctly by the method employed by Principal Forbes, MM. Despretz, Wiedemann, Franz, and others, which consisted in observing the temperature at different points of a long bar when one end had been kept at a constant temperature sufficiently long for the temperature of any one point of the bar to have become constant. But as the substances for experimenting on became less and less conducting, the amount of heat lost by radiation becomes larger and larger compared with that conducted along the bar; so that this method of experimenting fails altogether for a non-conducting substance like stone.

In such a case the plan usually adopted has been to measure the amount of heat conducted through a very thin wide sheet of the material when the temperature of each of its surfaces was kept constant. But even when considerable precautions are taken to prevent loss of heat from the edges, &c. (such as those employed by Professor G. Forbes in his experiments published in the Proceedings of the Royal Society of Edinburgh for February 1873), still we feel sure that the results must be

* Communicated by the Authors, having been read before the Asiatic Society of Japan, January 26, 1878.

Phil. Mag. S. 5. Vol. 5. No. 31. April 1878.

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somewhat doubtful. We are not, therefore, surprised to find the conductivity of marble to be 0.0048 (gramme, centimetre, second) as given by M. Péclet in 1841, to be 0.0097 for finegrained and 0.0077 for coarse-grained marble, as given by M. Despretz in 1853, and as 0.0017 as given by Prof. G.

Forbes in 1873.

The method employed by Principal Forbes, and Sir W. Thomson, in 1860, of deducing the conductivity of rock from observations of underground temperature is, of course, susceptible of much greater accuracy than the method referred to above; but it has the disadvantage that a considerable period of time is necessary for the completion of one experiment, and it can only be performed on a rather large depth of rock forming part of the earth's crust.

The following method which we have employed for determining the conductivity of heat in stone, and which was suggested by some remarks made by Sir W. Thomson when lecturing to the Higher Natural-Philosophy Class, in Glasgow, in 1874, has the great advantage of perfect certainty in the results; and it can be used with comparatively little difficulty for all bad conductors. The principle consists simply in keeping a ball of the material to be experimented on in a water (or other) bath at a constant temperature for a sufficient length of time for the whole ball to acquire the temperature of the bath; then suddenly removing the warm water and allowing a continuous rapid stream of cold water of constant temperature to flow round the outside of the ball, while timereadings of the temperature of some fixed point in the ball (for example, the centre) are taken as the ball slowly cools. Under these circumstances one of Fourier's well-known equations enables us to determine the internal conductivity of the ball, and the emissivity of the surface.

The obvious difficulty in this method of experimenting is to determine the temperature, say, at the centre of the ball, at successive intervals of time, without disturbing the flow of heat in the sphere. The comparatively small size of our balls of stone would make this difficulty very considerable if an ordinary thermometer were used; but those who have worked numerical illustrations of Fourier's results will see that the introduction into the ball of a thermometric junction attached to very fine leading wires cannot appreciably affect the general conditions. For absolute correctness it would be necessary to have a conical tubulure space of which the sides were coated with a substance impermeable to heat, extending from the surface of the ball to the centre, and terminating in a small spherical cavity at the centre, and to employ a thermometric

arrangement of such a nature as would not add to or subtract from the heat at the centre.

One thermoelectric junction being at the centre of the ball, the other may be either kept at a constant temperature, in which case the electric current will be a function of the difference of temperature between the junctions, their mean temperature, the position of the neutral point for the two metals employed, and the slope of their thermoelectric lines; or the other junction may be immersed in a compensating-bath, which, by being always kept at such a temperature that there is no current, indicates at any moment the temperature of the centre of the ball.

This latter, or balance, method was adopted, as it has the following advantages: first, the range of temperature through which the ball falls may be large, and still the galvanometer may be made as sensitive as we please; second, the balance method may be employed nearly without reference to the "thermoelectric power of the two metals at different temperatures; and, thirdly, since there is no current, no heat is added to or subtracted from the centre of the ball thermoelectrically, so that no vitiations of the theoretical conditions to ensure accuracy could occur except by heat-conductivity of the thin wires. In reality, of course, as it was impossible to cool the compensating-bath at exactly the same rate as the centre of the ball, there usually was a very weak current ; but as the junction in the bath was as often a very little hotter as a very little colder than that in the ball, the excessively small gains and losses of heat produced by the currents balanced one another.

However, our balance method was employed chiefly for the first two reasons, and not because we feared the abstraction of heat through thermo-electric currents.

II. Details of the Apparatus.-In Pl. IX. fig. 1, A is a stone ball 13.8 (thirteen and eight tenths) centims. in diameter, resting on three points in a metal water-bath, B, 17.5 (seventeen and a half) centims. high and 18.3 (eighteen and three tenths) centims. in diameter. This bath had a tap, R, for letting in cold water of constant temperature from a cistern, and a large opening, O, which could be closed by a cork, for suddenly emptying B. The bath stood in a tub, W, to catch the overflow, as will be described further on. At the centre of the stone ball there was a thermoelectric junction, C, of iron and copper, the wires being carefully insulated from the water and from one another except just at their extremities, where they were bound together and soldered, and immersed in a small drop of mercury to form good thermal contact with the stone.

The cylindrical hole in the stone through which the wires were inserted was only made just large enough to receive them; and the possibility of water entering the hole and making contact with the junction was prevented by the surface of the insulated wires being smeared over with a paste composed of white lead, red lead, and linseed-oil, which by hardening cemented the wires to the stone. The copper wire passed to a key, K, which was connected with one terminal, T, of a delicate deadbeat reflecting-galvanometer of about three quarters of an ohm resistance, which we had constructed for measuring thermal currents. The other end of the iron wire was bound and soldered at J to another copper wire, which was connected with the other terminal, T', of the galvanometer. DD was a copper compensating water-bath, by means of which the thermoelectric junction J could be always kept at the same, or nearly at the same, temperature as the other junction at the centre of the ball. To ensure the junction J quickly acquiring the temperature of the water in the bath DD, a small perforated plate of copper, P, was soldered to J and hung in the water without touching the sides or bottom of the bath. The bath was divided longitudinally by a perforated copper plate, QQ, to allow of the water being kept rapidly stirred (to ensure equality of temperature) without risk of the Kew standard thermometer S, which hung in the water, being broken.

This bath was fitted with two taps, U, V-the one for letting in cold water from the cistern, the other for emptying the bath. H is another thermometer hanging in the bath B, and having its bulb surrounded by a small metallic screen to shield it from direct radiation from the ball, but which allowed of free access of the water to the bulb. Either water-bath could be heated by suitable spirit-lamps.

III. Method of experimenting.-The two water-baths having been filled with water and left for a sufficiently long time for the temperature of all parts of the apparatus to have become uniform, or very nearly so, a reading of the galvanometer was taken, a small deflection d1 being obtained. This deflection was due to a small unknown difference of temperature t1 still remaining between the two junctions. The temperature of J was now raised by a number of small increments, to, tз, &c., producing deflections d2, ds, &c. respectively; then, since for small differences of temperature the currents are proportional to the differences, we have, if T is the difference of temperature corresponding with any small deflection D,

the object of taking the mean of a number of observations being, of course, to calibrate the scale near the zero-point with considerable accuracy. This determination of the sensibility of the galvanometer was made before every experiment; and it was usually found that one division of the scale corresponded to rather less than one fiftieth of a degree Centigrade difference of temperature between the junctions when the junctions themselves had a temperature of about 23° C. This amount of delicacy was really more than was absolutely necessary, since the thermometer in the compensating-bath could only be read to the twentieth of a degree.

The baths DD and B were now heated up to about 70° C., and kept at that temperature until the temperature of all parts of the stone ball had become uniform—that is, until there was no current when the two thermometers S and H indicated exactly the same temperature, the small scale-error in H being, of course, allowed for. At this moment the cork at O was removed, the tap R opened, and a quantity of cold water poured into B by means of the tube M M so as to flood the bath B; the whole of the warm water in B was therefore suddenly displaced by cold cistern-water. O was now closed but R left open, so that there was a continual stream of cold water flowing upwards and overflowing the bath at the top. Constant readings of the thermometer in the compensating-bath, combined with simultaneous readings of the galvanometer (the latter being kept as small as possible), were now taken for about 80 minutes, by which time the whole ball had cooled down nearly to the temperature of the cold water. By opening the key K the zero of the galvanometer was frequently taken, to detect any slight change. It was the duty of one observer solely to observe the galvanometer, of another to cool the compensating-bath DD at the right rate and to take readings of the thermometer suspended in it, and of a third to record the time together with the readings made by the other two, as well as to take occasional readings of the thermometer H.

IV. Reduction of the Readings.-Fourier's equation for the temperature of a point at a distance a centimetres from the centre of a homogeneous globe, when the globe has been initially all at constant temperature and when it is cooling by a constant external temperature being maintained, is