242 



NATURE 



{Jan. II, 1877 



to the relatively small conductivity of the portion (283 reet) 

 which is not rock salt. » The slow rate of increase observed in 

 the long interval between the depths of 2,100 and 3,390 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 — 



/ = 7-18 + flj; + bx^, 



t denoting the temperature (Reaumur) 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 — — "000000 1 25 79 1, 



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 

 Jrom the boldness of its reasoning in reference to the Sperenberg 

 observations. Prof. Mohr, however, does not quote the obser- 

 vations themselves, but only the temperatures calculated by the 

 above formula, which he designates, in his original paper {Ncuts 

 Jahrbuch fiir Mineralogie, Sec., 1875, Heft4), "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 boiing," a desig- 

 nation 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 pjyticular mode of reduction which was adopted, being a 

 mathematical consequence of the assumed formula if = 7-18 4- 

 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 i, 



Herr Dunker, in his ovi^n paper, lays no stress upon the for- 

 mula, 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 cither be suppressed or accompanied by the state- 

 ment 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 circula- 

 tion of water in bores, has lor 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 experi- 

 ments it is difficult to place much reliance on any observations 

 taken in deep bores without plugging. The selection of a suit- 

 able form of plug is now occupying the careful attention of your 

 Committee. 



Herr Bunker'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 beIo-.v 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 fo'-ce which was 

 found necessary for thus starting the plug, as well as the imnres- 

 sion 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 cuUing-tool. Herr Dunker remarks 

 that this plan is adapted to a soft material like rock-salt, but 

 that in ordinary hard rock it would be better to make the bot- 

 tom of the main bore flat, and to close the advance-bore by an 

 elastic disc 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 advance- 

 bore 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 ot 

 being pressed between two wooden discs, 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 sugc^estion of 

 bore-inspector Zobel, the pressure was applied and removed by 

 means of screwing. Two steel springs fastened to the upper 

 disc, 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 disc from turning, but 

 offered little resistance to its rising or falling. The lower disc, 

 on the contrary, was permitted to turn. Both discs were carried 

 by the iron boring-rods. Rotation of these in one direction 

 screwed the discs nearer together, and rotation in the other direc- 

 tion 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 rais- 

 ing 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 indian-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 Vjore, 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 01 

 bag ; but the water-bags were preferred, as returning more easily 

 to their original size when the pressure was removed, and conse- 

 quently being less liable to injury in extraction. In some obser- 

 vations since taken in another place (Sudenberg), Herr Dunker 

 states (in the private letter above referred to) that indian-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 in- 

 volved 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 re- 

 moved. 



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 prope 

 depth, by letting down upon it a sliding weight suspended by 

 second wire. Sir W. Thomson suggests that a series of indian 

 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 2,000 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 1,950 feet; and more recently 79° F. 



S 



