ON UNDERGROUND TEMPERATURE. 207 



t denoting the temperature (Reaumur) at the depth .^■ (Rhenish feet), and 

 has computed the most probable values of a and h by the method of least 

 bijuares. He finds 



a = -0129857 h= - -00000125791, 



the negative sign of h indicatiug that the increase of temperature becomes 

 sloAver 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 Spcreuberg observations. Prof. Mohr, however, 

 does not quote the observations themselves, but only the temperatures calcu- 

 lated by the above formula, which he designates, in his original paper (' Neuea 

 Jahrbuch fiir 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 arith- 

 metical 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 — 



< = 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 state- 

 ment that its author reserves a different deduction. 



The following are the differences between the temperatures computed by 

 tlie formula and the observed temperatures : — 



Difference (computed 

 Depth. minus observed). 



700 -1-621 



900 -1-931 



1100 -1-204 



1300 -f 0-427 



1500 -1-0-553 



1700 -f 0-882 



1900 -fO-811 



2100 +0-238 



3390 -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 con- 

 tained such palpable evidence of convection as to render them manifestly 

 ■useless for the purpose intended ; and iu 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 suitable form of plug is now 

 occupying the careful attention of your Committee. 



