DIRECT INVESTIGATIONS OF ISOSTASY 181 



its center of inertia at 39 miles), will satisfy the conditions as well as a 

 uniform compensation to a depth of 76 miles or 132 kilometers.-^ 



In 1913 Hayford and Bowie published a memoir on the effect of topog- 

 raphy and isostatic compensation on the intensity of gravitation.^^ For 

 105 stations they computed the effect of the topographic features of the 

 entire earth on attraction at the station and assumed uniformly dis- 

 tributed compensation complete at a depth of 113.7 kilometers, corre- 

 sponding to solution G of Mr. Hayford's investigations. This study was 

 begun before Mr. Hayford had reached the conclusion that 133 kilometers 

 is more probable than the smaller depth, but Hayford and Bowie show 

 that the difference in the conclusions reached would be negligibly small. 



While their results are confirmatory of the hypothesis of compensation, 

 studies of the intensity of gravitation are very inferior to the deflection 

 method for the determination of the depth of the level at whic;]i com- 

 pensation is complete. 



As in the former investigation, Hayford deduced residuals ; so here he 

 and Bowie obtain from comparison of observations and computations 

 what they call new method anomalies. These consist of observed in- 

 tensities less computed intensities plus a small constant systematic cor- 

 rection to the Helmert formula of 1901. This correction is onlv 0.009 

 dyne, and if it were applicable at the equator would reduce gravity there 

 to 978.039 dynes.^" Like the residual, an anomaly lumps together all 

 sorts of errors of assumption and observation. Two of its components 

 are of special geological importance. If compensation is supposed com- 

 plete and there were no errors in maps or mean density and the like, then 

 for a given region the new method anomaly, if positive, would indicate 

 excess of material or of pressure, an overload. Similarly a negative 

 anomaly would be interpreted as a deficiency of mass in the column 

 underlying the surface area; but an anomaly might equally well be due 

 to irregular distribution of compensation. A very moderate batholith of 

 peridotite just below the station might be accurately compensated by 

 deficiency of mass at a depth of 50 miles so that there would be complete 



2* Although these compensating excesses or deficiencies of matter cannot be considereil, 

 strictly speaking, as concentrated at their centers of inertia, the depths of these points 

 are not very different ; 40 miles for the thin layer, 89 for the wedge, 38 for a shell 

 reaching the surl'acc. 



^ The effect of topography and isostatic compensation on the intensity of gravity. 

 Coast and Oeod. Siirv., IDlL'. 



=«* Helmert's foriimla ol' IDOl, <.ii Hit- Potsdam system, for the tlicori'tical value of 

 gravity at seaJevd is 



yo = 978.030 ( 1 4- Ii.il()o30'2 sin^ <f> — O OOOOOT sin- ■-' </)) 



The corresponding formula of Hayford and Bowie on which tlulr "new method anom- 

 alies" are based is 



7u ^ 978.039 (I + U0o302 sin* <f> — O.0O0OO7 sin- ■! </>). 



