104 Bowie — Recent Gravity Work in the United States. 



Earth and Isostasy" that the apparent deflections are increased 

 by considering only the attraction, positive and negative, of the 

 topography alone. In his solution II the effect of the negative 

 attraction of the defect of mass under the continents was 

 applied in addition to the effect of the topography, as was also 

 the positive attraction of the excess of mass under the oceans, 

 and the deflections were greatly reduced. 



The theory of isostasy postulates that each topographic fea- 

 ture is compensated for hy a variation from the normal density 

 below sea level. The crust of the earth under a land area has 

 a deficiency of mass and that under a water area has an excess 

 of mass. It is assumed that the mass is the same in each, unit 

 column extending from the actual surface of the earth, land or 

 water, to a certain depth below sea level. This statement is 

 based upon the theory that there is complete local compensa- 

 tion uniformly distributed with respect to depth. Of course, 

 the actual condition deviates somewhat from this ideal. The 

 compensation for a feature, a separate mountain mass for exam- 

 ple, is not necessarily directly under it, nor is the compensation 

 distributed absolutely uniformly and absolutely limited by a 

 certain depth. The second investigation of the figure of the 

 earth by Hayford gave 120*9 kilometers as the most probable 

 limiting depth. He predicted that " future investigations will 

 show that the maximum horizontal extent which a topographic, 

 feature may have and still escape compensation is between one 

 square mile and one square degree. The introduction of the 

 theory of isostasy to the investigations doubled the weight of 

 the resulting value for the flattening of the earth, which was 

 found to be l/297-0±'5. 



Having met with such success in the investigations of the 

 figure of the earth, it was decided to apply the theory of isos- 

 tasy in the reductions of the gravity stations in the United 

 States. This was done for 56 stations by Hayford in 1909. A 

 preliminary report upon the results of his investigation was 

 read at the meeting of the International Geodetic Association 

 at London and Cambridge in 1909.* 



The intensity of gravitation increases with the distance from 

 the equator, it decreases with the increase in elevation above 

 sea level and is affected by the topography of the world and its 

 compensation. 



The gravity for any latitude is given by Helmert's formula 

 of 1901 : 



* Published in Comptes Rendus des Seances de la seizieme Conference 

 generale de L' Association Gebdesique Internationale reunie a Londres et a 

 Cambridge du 21 au 29 Septembre 1909. Rediges par le Secretaire perpetuel 

 H. G. Van de Sande Bakhuyzen. I er Volume : Proces-verbaux et rapports 

 des Delegues sur les travaux geodesiques accomplis dans leurs pays, pp. 354- 

 390. 



