DIRECT INVESTIGATIONS OP ISOSTASY 183 



never be quite free from the suspicion of some hidden fallacy, while a 

 result obtained by independent methods commands great confidence. 



Mr. Helmcrt's method, printed as long ago as 1909,^^ is applicable only 

 at selected stations, Avliere a rather level coastal plain and a tolerably 

 deep sea are connected by a fairly smooth and steep slope. The coast 

 must also be assumed to be part of a great circle. On the hypothesis 

 that there is a level of isostatic compensation, it is easy to prove that in 

 such a region the intensity of gravity will reach a maximum at the shore 

 and a minimum at the junction of the submarine slope with the level 

 sea-bottom; and from the observations it is possible to make a choice 

 between various assumptions as to the depth of the level of isostatic 

 compensation. Like Hayford, Helmert prefers the hypothesis that com- 

 pensation is uniformly distributed. 



IMr. Helmert found on record 51 localities, widely distributed over 

 the world, which were suitable for treatment by his method. From them 

 lie deduced for the depth of the level in (|uestion as a simple mean 

 118 d= 2;;J kilometers; but he tonk tlio superficial density of the earth at 

 2.73, while Hayford assumed it at 2.67. In a second paper Helmert so 

 modified Hayford's equations as to render them suitable for the compu- 

 tation of the mean and probable errors and, with the superficial density 

 2.67., derived from them a depth of 123.5 ± 14 kilometers mean error.'"*^ 

 Assuming the same superficial density of the earth, Helmert finds from 

 his own investigation 124 ± 22 kilometers mean error. That the two 

 results substantiate one another is evident ; indeed, so close an agreement, 

 apart from the error, must be considered accidental, and in later papers 

 Helmert rounds off the figures to 120 kilometers. He points out that 

 his mean error of ± 22 kilometers is larger than Hayford's and suggests 

 that this may be due to the world-wide distribution of his stations.^® 



At Mr. Helmert's instance, Mr. 0. Hecker made several voyages in 

 the first years of the century for the purpose of determining the intensity 

 of gravity at sea. The method employed was devised by Mr. H. Molin, 

 who found that the gravity correction of the quicksilver barometer on 

 land could be determined by the help of the boiling-point thermometer.^'"' 

 This method carried out on a moving vessel is not of a high degree of 



^Sitznngsber. k. Preuss. Akad. der Wiss.. lilOO, July to Doc. p. 1192. 



3* The probable error as derived from the theory of least squares is ± kilometers. 

 The actual errors are probably larger than the probable eri-ors because of undetected 

 systematic errors. As I understand it, Helmert takes (he moan error in order to leave a 

 margin for undetected errors. The difference is a mere estimate, not a conclusion from 

 theory. The mean error is 1.4S2fi times the prnbnble error. 



■'^■' Sltzungsbor. k. I'reuss. Akad. dor Wiss., 1011. .T.in. to .rune. p. 10. 



■"^ Sltzungsber. k. Preuss. Akad, der Wls.s., 1902, p. 120, and Enoyc. der Math. Wiss., 

 vols. 6, 1, 7, p. 125. 



