456 On the Rate of Increase of Underground Temperatures. 



With the view of summing up his results in small compass, 

 Herr Dunker has assumed the empirical formula : 



*=7-18 + aa; + fe2 ) 

 t denoting the temperature (Reaumur) at the depth x (Ehenish 

 feet) ; and has computed the most probable values of a and b. bv 

 the method of least squares. He finds 



a — -0129857 b = — '0000001 25791, 



the negative sign of b indicating that the increase of tempera- 

 ture becomes slower as the depth increases. 



A paper by Prof. Mohr, of Bonn, as represented by an ab- 

 stract published in Nature (vol. xii, p. 545), lias attracted atten- 

 tion 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 calcu- 

 lated by the above formula, which he designates, in his original 

 paper (Neues Jahrbuch fur Mini-rahyk, etc., 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 

 incfl :.. ::ts of temperature for successive equal increments of 

 depth, form an exact arithmetical progression, as if this were a 

 tie fact of observation, whereas it is merely the result 

 of the particular mode of reduction which was adopted, being a 

 Leal consequence of the assumed formula t = 718 + 

 ax + bx 2 . 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 for- 

 mula, and gives a caution against extending it to depth- much 

 'in those to which the observations extend. Writing 

 to Plot. Kveret 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 it,, author iv„ ,\,.. ; , dilf.Mvnt deduction. 



The following are the differences between the ten 

 computed by the formula and the observed temperatures : 



