Assuming, with Herr Dunker, the mean temperature of the surface to be 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 fect is exactly 1° Fahr. 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 + bx2,

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

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 + bx2.

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:

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, nailed 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-tool. 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 (Sudenberg), Herr Dunker states (in the private letter above referred to) that

india-rubber bags, filled with water, and pressed, not by screwing, but by the weight of the rods, were employed with much satisfaction.

All the methods of plugging employed by Herr Dunker involved the use of the iron rods belonging to the boring-apparatus, and therefore would be inapplicable (except at great expense) after the operation of boring is finished. and the apparatus removed.

It seems desirable to contrive, if possible, some plug that can be let down and raised by a wire. In the first report of your Committee, it was suggested that two bags of sand, one above and the other below the thermometer, should be used for this purpose. Bags of sand, however, would be liable to rub off pieces from the sides of the bore, and thus to become jammed in drawing up. Mr. Lebour has devised a plug which will be of small diameter during the processes of lowering and raising, but can be rendered large and made to fit the bore, when at the proper depth, by letting down upon it a sliding weight suspended by a second wire. Sir W. Thomson suggests that a series of india-rubber disks, at a considerable distance apart, will probably be found effectual.

Mr. Boot has continued his observations in the bore which he is making at Swinderby, near Scarle (Lincoln). It has now been carried to the depth of 2000 feet, and is in earthy limestone or calcareous shale, of Carboniferous age. Its diameter in the lower part is only 3 inches. In April last the temperature 78° F. was observed at 1950 feet; and more recently 79° F. was observed at 2000 feet-the water, in each case, having been undisturbed for a month. Supposing these results not to be vitiated by convection, and assuming the mean temperature at the surface to be 50°, we have an increase of 29° in 2000 feet, which is at the rate of 1o in 69 feet.

Mr. Symons has taken a series of observations at the depth of 1000 feet in the Kentish-Town well, with the view of determining whether the temperature changes. The instrument employed is a very large and delicate Phillips's maximum thermometer. The following is a list of the observations:

The "depth indicated" is shown by a measuring wheel or pulley, over which the wire runs by which the thermometer is raised and lowered, as described, with a diagram, in the Report for 1869. The above Table shows that there is always some stretching, real or apparent, in the interval between lowering the thermometer and raising it again. Recent observations, by means of a fixed mark on the wire, have shown that the change is not, in the main, a permanent elongation, but an alternation of length. It is probably due in part to the greater tension which the wire is under in raising than in lowering, a circumstance which will cause a temporary difference of length variable with the rapidity of winding up; also in part to the circumstance that the wire is warmer when it has just left the water than when it is about to be let down. Some portion of the irregularity observed may be due to variations of temperature in that part of the well (210 feet) which contains air. The observations, taken as a whole, show that any variations of temperature which occur in this well at the depth of 1000 feet are so small as to be comparable with the almost inevitable errors of observation. The observations will be continued at intervals of six months, with additional precautions, and with an excessively slow (specially constructed) non-registering thermometer, in addition to the maximum thermometer hitherto employed.

Through the kindness of the eminent geologist M. Delesse, of the École Normale at Paris, observations have been obtained from the coal-mines of Anzin, in the north of France. They were taken under the direction of M. Marsilly, chief engineer of these mines. Maximum thermometers of the protected Negretti pattern were inserted in holes bored horizontally to the depth of 6 or 7 of a metre in the sides of shafts which were in process of sinking, and in which there was but little circulation of air. A quarter of an hour was allowed to clapse in each case, after the boring of the hole, before the thermometer was inserted and the hole plugged. Four different shafts were tried. Those designated as Nos. I., II., III. were in the mine Chabaud La Tour, and No. IV. was in the mine Renard.

In shaft I. observations were taken at eight different depths, commencing with the temperature 564° F. at a depth of 38.5 metres, and ending with 673° F. at 200-5 metres.

In shaft II. there were observations at four depths, commencing with 55° at 873 m., and ending with 634° at 185 m.

In shaft III. there were observations at three depths, commencing with 56° at 87.8 m., and ending with 62° at 144 m.

These three shafts, all belonging to the same mine, were very wet, and the temperature of the air in them was 11° or 12° C. (52° or 54° F.).

In shaft IV., which was very dry and had an air temperature of about 15° C. (59° F.), observations were taken at six depths, commencing with 703° F. at 21-2 m., and ending with 84° F. at 134.8 m.

The mean rates of increase deduced from these observations are:

In Shaft I., 1° F. in 14.4 m., or in 47.2 fect.

II.,
III.,
IV.,

11.5 m., 8.65 m,

The observer mentions that in shaft II. there was, at a depth of 90 m., a seam of coal in which heat was generated by oxidation; but no such remark is made with respect to any of the other shafts, although it is obvious that some disturbing cause has rendered the temperature in shaft IV. abnormally high. Possibly the heat generated in boring the holes for