« EelmineJätka »
Ninth Report of the Committee, consisting of Prof. EVERETT, Sir W.
Thomson, F.R.S., Prof. J. CLERK MAXWELL, F.R.S., G. J. SYMONS, F.M.S., Prof. RAMSAY, F.R.S., Prof. A. GEIKIE, F.R.S., JAMES GLAISHER, F.R.S., GEORGE Maw, F.G.S., W. PENGELLY, F.R.S., Prof. HULL, F.R.S., Prof. ANSTED, F.R.S., Prof. PRESTWICH, F.R.S., Dr. C. LE NEVE FOSTER, Prof. A. S. HERSCHEL, G. A. LEBOUR, F.G.S., and A. B. WYNNE, appointed for the purpose of investigating the Rate of Increase of Underground Temperature downwards in various Localities of Dry Land and under Water.
Drawn up by Prof. EVERETT, Secretary. A REMARKABLE series of observations have recently been taken in a boring at Sperenberg, near Berlin. The bore was carried to the depth of 4052 Rhenish (or 4172 English) feet, and was entirely in rock-salt, with the exception of the first 283 fcet, which were in gypsum with some anhydrite. The observations were taken under the direction of Herr Eduard Dunker, of Halle an der Saale, and are described by him in a paper occupying thirtytwo closely printed quarto pages (206–238) of the • Zeitschrift für Berg-, Hütten- und Salinen-Wesen' (xx. Band, 2 and 3 Lieferung: Berlin, 1872).
The instrument employed for measuring the temperatures was the earththermometer of Magnus, which gives its indications by the overflowing of mercury, which takes place when the instrument is exposed to a higher temperature than that at which it was set. To take the reading, it is immersed in water a little colder than the temperature to be measured; the temperature of this water is noted by means of a normal thermometer, and at the same time the number of degrees that are empty in the earth-thermometer is noted. From these data the maximum temperature to which the instrument has been exposed can be deduced, subject to a correction for pressure, which is not very large, because the same pressure acts upon the interior as upon the exterior of the thermometer.
In the following résumé (as in the original paper) temperatures are expressed in the Réaumur scale, and depths in Rhenish feet, the Rhenish foot being 1.029722 English fout.
Observations were first taken, at intervals not exceeding 100 feet, from the depth of 100 feet to that of 4042 feet, the temperature observed at the former depth being 11°, and at the latter 380.5; but all these observations, though forming in themselves a smooth series, were afterwards rejected, on the ground that they were vitiated by circulation of water and consequent convection of heat.
It has often been supposed that though this source of error may affect the middle and upper parts of a bore, it cannot affect the bottom; but the Sperenberg observations seem to prove that no such exemption exists. When the bore had attained a depth of nearly 3390 feet, with a diameter of 12 inches 2 lines at the bottom, an advance-bore of only 6 inches diameter was driven 17} feet further. A thermometer was then lowered halfway down this advance-bore, and a plug was driven into the mouth of the advance-bore so as to isolate the water contained in it from the rest of the water above. After twenty-eight hours the plug was drawn and the thermometer showed a temperature of 36°:6. On the following day the temperature was observed at the same depth without a plug, and found to be 330.6. Another observation with the plug was then taken, the thermometer (a fresh instrument) being left twenty-four hours in its position. It registered 36o.5, and again, without
plugging, it gave on the same day 33°.9. It thus appears that the effect of convection was to render the temperature in the advance-bore 3° R. too low,
Apparatus was then employed for isolating any portion of a bore by means of two plugs at a suitable distance apart, with the thermometer between them. This operation was found much more difficult than that above described ; but in several instances it gave results which were deemed quite satisfactory : while in other instances the apparatus broke, or the plugging was found imperfect. The deepest of the successful observations by this method was at 2100 feet, and the shallowest was at 700 feet. The first 444 feet of the bore were lined with iron tubes, between which the water had the opportunity of circulating even when the innermost tube was plugged ; hence the observations taken in this part were rejected. - All the successful observations are given in the third column of the following Table, subject to a correction for pressure; and, for the sake of showing the error due to convection in the ordinary mode of observing, the temperatures observed at the same depths when no plugs were used are given in the second column :
These temperatures are not corrected for pressure, but they are corrected for rise of zero in the normal thermometer; and this last circumstance explains the difference of 0.4 between the temperature 360:15 here given and 369.55, which is the mean of the above-mentioned observations at the depth of 3390 feet.
Another proof of the injurious effect of convection was obtained by comparing the observed temperatures (without plugging) in the first 400 feet of the great bore, designated Bore I., with the temperatures observed at the same depths during the sinking of another bore, designated Bore II., near it, the observations in this latter being always taken at the bottom. The following were the results :
Bore I. Bore II.
11.6 10.4 300 .............
12:3 11:5 400 .................. 13.6 12.5 The temperature at the depth of 100 feet in the great bore thus appears to have been raised about 2° R. by convection.
The following is a Table of the successful observations, corrected for pressure :
28.668 3390 ............
37.238 Assuming, with Herr Dunker, the mean temperature of the surface to be 770.18, which is the mean annual temperature of the air at Berlin, we have the following increments of temperature with depth :
• The mean rate of increase found by comparing the temperatures at the surface and 3390 feet is exactly 1o Fabr. for 50 Rhenish or 51.5 English feet.
The numbers in the last two columns exhibit upon the whole a diminution with increase of depth; in other words, the temperature increases less
rapidly as we go deeper down. As regards the first 700 feet, which exhibit · a decidedly more rapid rate than the rest, it must be remembered that nearly half of this distance was in a different material from the rest of the bore, being in gypsum with some anhydrite, while all the rest was in rock-salt. Prof. Herschel has found, in recent experiments not yet published, that the conductivity of rock-salt is exceedingly high; and theory shows that the rates of increase, in superimposed strata, should be inversely as their conductivities. We may therefore fairly attribute the rapid increase in the first 700 feet to the relatively small conductivity of the portion (283 feet) which is not rock-salt. The slow rate of increase observed in the long interval between the depths of 2100 and 3390 feet is not so easily accounted for; we can only conjecture that this and the other inequalities which the above Table presents, for depths exceeding 700 feet, are due to fissures or other inequalities in the rock which have not been put in evidence.
With the view of summing up his results in small compass, Herr Dunker has assumed the empirical formula
t = 7.18 + ax + bx?,
t denoting the temperature (Réaumur) at the depth x (Rhenish feet), and has computed the most probable values of a and b by the method of least squares. He finds
a= .0129857 b= - .00000125791, the negative sign of b indicating that the increase of temperature becomes slower as the depth increases.
A paper by Prof. Mohr, of Bonn, as represented by an abstract published in Nature' (vol. xii. p. 545), has attracted attention from the boldness of its reasoning in reference to the Sperenberg observations. Prof. Mohr, however, does not quote the observations themselves, but only the temperatures calculated by the above formula, which he designates, in his original paper (Neues Jahrbuch für Mineralogie,' &c., 1875, Heft 4), “ the results deduced from the observations by the method of least squares.” In the abstract in • Nature' they are simply termed " the results of the thermometric investigation of the Sperenberg boring," a designation which is still more misleading.
Attention is called to the circumstance that the successive increments of temperature for successive equal increments of depth form an exact arithmetical progression, as if this were a remarkable fact of observation, whereas it is merely the result of the particular mode of reduction which was adopted, being a mathematical consequence of the assumed formula
t= 7-18 + ax + bx?. The method of least squares is not responsible for this formula, but merely serves, after this formula has been assumed for convenience, to give the best values of a and b.
Herr Dunker, in his own paper, lays no stress upon the formula, and gives a caution against extending it to depths much greater than those to which the observations extend. Writing to Prof. Everett under date April, 1876, he requests that, in the summary of his results to be given in the present Report, the formula should either be suppressed or accompanied by the statement that its author reserves a different deduction.
The following are the differences between the temperatures computed by the formula and the observed temperatures :
- 1.204 1300
....................... -0.482 The necessity of adopting some means to prevent the circulation of water in bores has for some time been forcing itself upon the attention of your Committee. Many of the observations taken by their observers have contained such palpable evidence of convection as to render them manifestly useless for the purpose intended ; and in the light of the Sperenberg experiments it is difficult to place much reliance on any observations taken in deep bores without plugging. The selection of a suitable form of plug is now occupying the careful attention of your Committee.
Herr Dunker's paper gives a very full account of the different kinds of plug employed at Sperenberg.
For stopping the mouth of the advance-bore the plug had a tapering shape, and was of hard wood, strengthened by two iron rings, one at each end, and covered with a layer of tow 5 lines thick, outside of which was thick and strong linen, pailed above and below to the wood through a leather strap. It was lowered into its place by means of the iron rods used for boring; and, when in position was pressed home by a portion of the weight of the rods. The plug carried the thermometer suspended from it. Its extraction was commenced by means of a screw on the beam of the boring-machine, in order to avoid a sudden jerk, which might have broken the thermometer. The force which was found necessary for thus starting the plug, as well as the impression observed upon it when withdrawn, showed that it had fitted tight. To insure a good fit, the top of the advance-bore had been brought to a suitable shape, and its inequalities removed, by means of a revolving cutting-too). Herr Dunker remarks that this plan is adapted to a soft material like rocksalt, but that in ordinary hard rock it would be better to make the bottom of the main bore flat, and to close the advance-bore by an elastic disk pressed over it. The method of observation by advance-bores can only be employed during the sinking of the bore, a time when it is difficult to avoid error arising from the heat generated in boring. The expense of making an advancebore at each depth at which an observation is required is also an objection to its use.
Another kind of plug devised by Herr Dunker, and largely used in the observations, consisted of a bag of very stout india-rubber (9 millimetres thick) filled with water, and capable of being pressed between two wooden disks, one above and the other below it, so as to make it bulge out in the middle and fit tightly against the sides of the bore. On the suggestion of bore-inspector Zobel, the pressure was applied and removed by means of screwing. Two steel springs fastened to the upper disk, and appearing, in Herr Dunker's diagram, very like the two halves of a circular hoop distorted into an oval by pressing against its walls, prevented the upper disk from turning, but offered little resistance to its rising or falling. The lower disk, on the contrary, was permitted to turn. Both disks were carried by the iron boring-rods. Rotation of these in one direction screwed the disks nearer together, and rotation in the other direction brought them further apart. The india-rubber bag could thus be made to swell out and plug the bore when it was at the desired depth, and could be reduced to its original size for raising or lowering. In order to prevent the boring-rods from becoming unscrewed one from another, when rotated backwards, it was necessary to fasten them together by clamps, a rather tedious operation in working at great depths.
In taking observations at other points than the bottom, two of these plugs were employed, one above and the other below the thermometer.
In some of the experiments, the apparatus was modified by using linen bags filled with wet clay, instead of india-rubber bags filled with water; and, instead of screwing, direct pressure was employed, the lower disk being supported by rods extending to the bottom of the bore, while the upper disk could be made to bear the whole or a portion of the weight of the rods above it. Some successful observations were obtained with both kinds of bag; but the water-bags were preferred, as returning more easily to their original size when the pressure was removed, and consequently being less liable to injury in extraction. In some observations since taken in another place (Sudeoberg), Herr Dunker states in the private letter above referred to) that