388 On Capt, Rater's Experiments on the Pendulum. [May, 



height of the station at Unst was found to be 28 feet above low 

 water ; whence we have 0*12 for the correction, as deduced from 

 the squares of the distances from the earth's centre \ and as the 

 station at Unst was surrounded by hills composed of serpentine, 

 I shall take 0*12 x i = 0*06 for the correction to be applied in 

 order to obtain the number of vibrations which would be made 

 at the level of the sea.— (Phil. Trans. 1819, Pint III. p. 354.) 



Here it is surely obvious that he introduces the consideration 

 of the nature of the hills surrounding his station, not for the pur- 

 pose of applying a correction for Iheir attraction, but as afford- 

 ing a presumption of what might be the nature of the substratum 

 of the place of observation ; — a consideration which Dr. Young's 

 rule requires to be introduced, as the correction varies not only 

 with the nature of the eminence, but also with its density. 



Having thus attempted to make out that Capt. K. has mistaken 

 and misapplied Dr. \ .'s rule, this writer next proceeds to find 

 fault with the quantitij deduced from the rule. After quoting 

 Dr. YAs account of his correction from the Phil. Trans. 1819, 

 Part I. p. 93, and stating that the correction for a tract of table 

 land of a mile in thickness will be -^-^-^^ of the whole correction 

 for elevation ; he proceeds to remark, " If this be the case, we 

 cannot perceive the grounds on which Capt. K. takes -i, only a 

 little less than-j%^^ for the correction applicable to an elevation of 

 28 feet, in the actual state of the superficial inequalities. We 

 may have overlooked some step in his reasoning, or Dr. Y.'s ; 

 but we feel bound to state our difficulty as it occurs." 



. There is doubtless some difficulty in the case; but from Dr. 

 Y.'s own words, it appears that he considers " that for a ])lace 

 situated on an elevated table land of a mile in thickness, of the 

 Tuean density of the earth, the allowance for elevation would be 

 reduced to one-half; and in almost any country that could be 

 chosen for the experiments, it must remain less than three 

 fourths of the whole correction deduced immediately from the 

 duplicate proportion of the distances from the earth's centre." 

 Thus the correction (as Capt. K. remarks) will vary according to 

 the nature of the elevation, and also its density from one-half to 

 three-fourths of the quantity before deduced. In any situation 

 it will not be reduced less than one-half; nor more than three- 

 fourths. These considerations seem to have been overlooked by 

 this writer ; still, however, I do not mean to assert, that the 

 numbers are absolutely correct. It is to be wished that both 

 Capt. K. and Dr. Y. had given a more detailed account of the 

 method of finding this correction. 



In a subsequent page (347), this writer observes ; '' from the 

 great disturbmg force at Arbury Hill, we may infer that there 

 exists very near it a mass of matter of considerable density. 

 Capt. K. conjectures that this mass is Mount Sorrel, which con- 

 sists of granite, and other rocks of primitive formation are 

 situated in its vicinity." 



