154 JOSEPH BARRELL 



Of the two other principal methods of gravity reduction which 

 have been previously used, the Bouguer reduction takes no account 

 of isostatic compensation, postulating a high rigidity of the earth's 

 crust, and neglects all curvature of the sea-level surface. The 

 ''free-air" reduction assumes that each piece of topography is 

 compensated for at zero depth. These two reductions correspond 

 thus to the hmiting solutions tried for deflections of the vertical. 

 The sum of the squares of the new method anomalies, when com- 

 pared respectively with the similar sums derived from the hypothesis 

 of rigidity and the hypothesis of compensation at depth zero, shows 

 that the assumption of isostatic compensation uniformly dis- 

 tributed to a depth of 114 km. gives on the average smaller 

 anomalies; is therefore much more probable and yields a more 

 accurate value for the intensity of gravity. The mean anomaly of 

 all stations in the United States without regard to sign, omitting the 

 exceptionally large anomalies of the Seattle stations, is as follows: 



New method o. oiS dyne^ 



Bouguer o. 063 



Free air o. 028 



The value of gravity for the United States Coast and Geodetic 

 Survey office at Washington was determined as 980 .112 dynes per 

 gram. The mean new-method anomaly is consequently about 

 o . 00002 of the value of gravity. The probable error of observation 

 and computation is about 0.003 dyne. The errors may, however, 

 frequently exceed o . 004 dyne and in rare cases may be as great as 

 o.oio dyne.^ The fact that these measures of gravity are the 

 forces acting on one gram will be understood through the rest of 

 the paper. 



Of the 124 stations, 32 have anomalies between 0.020 and 0.030, 

 12 have anomalies between 0.030 and 0.040.^ Still smaller num- 

 bers of stations have higher anomalies. These anomalies measure 

 departures in the earth's crust from the conditions of isostasy which 

 were postulated. In the interpretation of the anomalies in terms 

 of mass it is shown that a small excess of mass immediately below 



^ Bowie, 1912, p. 12. 



* Hayford and Bowie, 1912, p. 79; Bowie, 1912, p. 13. 



3 Bowie, 1912, p. 13. 



