400 ANNUAL. REPORT SMITHSONIAN INSTITUTION, 1910. 



Putnam himself stated in his article that the residuals obtained by 

 his computation was not precise. 



In order to understand this qualification of their results it is neces- 

 sary to consider the method of reducing the " mean plain." The 

 position of that plain is such that the masses represented by hills, 

 mountains, or plateaus above it are equal to the defects of mass 

 represented by valleys or wider depressions below it. The position 

 is calculated from topographic maps, whose accuracy thus enters 

 into the computation, but a more important factor is the radius of 

 the area about each station to which the estimate is extended. Gil- 

 bert took a radius of 30 miles and Putnam a radius of 75 miles, both 

 investigators being limited by the labor of computation to a smaller 

 area about each station than they would have chosen. Hayford has 

 since shown that the attractions due to topographic features out to 

 a distance exceeding 2,500 miles are not negligible, and for a work 

 on the intensity of gravity in the United States, which is the latest 

 published, he has extended the computations to the features of the 

 entire globe. Thus the detailed residuals of gravity, the differences 

 from the normal, obtained by Putnam and Gilbert, are suggestive 

 rather than precise. Those investigators proved the isostatic balance 

 of large features, but they did not demonstrate how small a feature 

 may be isostatically balanced or how large a feature may be rigidly 

 supported. 



We have thus compared the hypothesis of high rigidity of the 

 earth's crust with that of partial isostatic balance, entirely to the 

 advantage of the latter. There remains the hypothesis of complete 

 isostatic compensation, which postulates that all parts of the earth 

 are nicely balanced. Hayford has employed this assumption as the 

 basis of the most refined and extensive investigations as yet made on 

 the subject. 



The data which he has used are. derived from the work of the 

 United States Coast and Geodetic Survey and the computations have 

 been executed by that organization. There are two elaborate investi- 

 gations. One relates to deflections of the plumb line from the true 

 vertical as determined at 507 stations of the precise triangulation 

 which is the basis of the geodetic survey of the United States. 1 The 

 other investigation relates to observations with the pendulum for 

 gravity. 2 



Deflections of the plumb line are determined in precise triangula- 

 tion by comparing the direction of the apparent vertical line with 

 the true vertical which is fixed astronomically. 



1 Hayford, J. F. The figure of the earth and isostasy from measurements in the 

 United States. U. S. Coast and Geodetic Survey, Washington, 1909. 



2 Hayford, J. F. Supplementary investigation in 1909 of the figure of the earth and 

 isotasy. Coast and Geodetic Survey, Washington, 1910. 



