702 



SCIENCE 



[N. S. Vol. XXXIX. No. 1011 



section and the depth of the unit columns 

 which are supposed to have equal masses, 

 have not yet been accurately determined. 



The depth of compensation is probably 

 somewhere between one hundred and ten 

 and one hundred and thirty kilometers. 



It is reasonably certain that the com- 

 pensation is not always complete nor 

 always uniformly distributed to the depth 

 of compensation. (The above statements 

 are, of course, intended to apply only to 

 the area of the United States. Later on a 

 brief statement will be made in regard to 

 the rather limited results obtained in the 

 other countries.) But the average condi- 

 tions in the United States indicate a close 

 approximation to those postulated. 



The application of isostasy reduced con- 

 siderably the apparent anomalies, or de- 

 flections, in the United States and Hayford 

 was able to compute a figure of the earth 

 which is generally considered one of the 

 best, and probably the very best, now exist- 

 ing. His dimensions^ are: 



Equatorial radius, 6,378,388 ± 18 meters. 

 Polar semi-diameter, 6,356,909 meters. 

 Eeciprocal of flattening, 297.0 ± 0.5. 



The application of isostasy to the reduc- 

 tion of the gravity observations has reduced 

 the average anomaly in the United States 

 to 0.018 dyne, and at only one station is 

 the anomaly greater than 0.060 dyne. It 

 is, therefore, now possible to compute a 

 value for gravity at any point in this 

 country with an uncertainty of 0.018 dyne. 

 By either of the previous two generally 

 used methods of reduction, in which isos- 

 tasy was not employed, the average anom- 

 aly in the United States was much greater.* 



''See p. 54, ' ' Supplemental Investigation in 

 1909 of the yigure of the Earth and Isostasy. ' ' 



8 The average free air anomaly was 0.028 dyne 

 and the average value of the Bouguer anomaly 

 was 0.063 dyne. 



The largest free air anomaly was 0.216 

 dyne and there were five other anomalies 

 with values greater than 0.100 dyne. 

 There were five Bouguer anomalies 

 greater than 0.200 dyne and twenty-eight 

 other anomalies greater than 0.100 dyne. 

 It was found from the anomalies developed 

 by the investigations of deflections and of 

 gravity that there was no apparent rela- 

 tion between the topography and the size 

 and sign of the anomalies nor between the 

 anomalies and the areas of erosion or depo- 

 sition. Some relations to the geological 

 formation were developed.^ 



A severe test of the new method of re- 

 duction of gravity observations, with isos- 

 tasy considered, was the determination of 

 the flattening of the earth, from the stations 

 in the United States alone. The resulting 

 value is 1/298.4. This value agrees almost 

 exactly with Helmert's value of 1/298.3 

 which resulted from a consideration of 

 gravity stations widely scattered over the 

 earth and with a great range in latitude. 

 The anomalies by each of the older methods 

 of reduction, in which isostasy is ignored, 

 gave values which differed greatly from the 

 generally accepted best values. 



A brief statement of the method of ma- 

 king the gravity observations and of the 

 accuracy attained will suffice. All of the 

 stations in the United States used in the 

 recent investigations had gravity determined 

 by means of the quarter-meter invariable 

 pendulum^" which makes an oscillation in 

 approximately one half second. It is a 

 modification of the pendulums devised by 



9 See pp. 18-21 of ' ' Effect of Topography and 

 Isostatie Compensation upon the Intensity of Grav- 

 ity" (second paper). 



10 This pendulum and its case are described in 

 App. 1, Eeport of the Superintendent of the Coast 

 and Geodetic Survey for 1894, by G. R. Putnam. 

 The method of obtaining the flexure of the case 

 and the support is described in App. 6 of the Ee- 

 port for 1910, by W. H. Burger. 



