698 WILLIAM HERBERT HOBBS 



His positive argument and the facts upon which it is based. — ■ 

 Hayford's earlier studies have dealt with the well-known differences 

 between the astronomic and the geodetic determinations of latitude, 

 longitude, and azimuth — so-called deflections of the vertical — 

 measured first at 267 stations, and in a supplementary study at 

 116 stations, making in all 383, which are fairly well distributed 

 over the domain of the United States. These uncorrected residuals 

 have values which when expressed in terms of astronomic 

 minus geodetic determination (A-G) range between — 26'' 50 and 

 +3 2 ''43, the average being, however, comparatively small. The 

 later monographs have dealt with pendulum determinations of 

 gravity, made at 89 stations in the first study and 35 1 in the second, 

 a total of 124. Unfortunately, instead of correcting the measure- 

 ments of gravity so as to take account of both altitude and topog- 

 raphy and obtain a comparison of observed and computed values, 

 Hayford has combined with the correction for topography one for 

 "compensation" with reference to the assumed limiting surface 

 at a depth of 76 miles below sea-level. Fact and theory have thus 

 been combined in his tables in such a way as to make it impossible 

 to extricate the figures representing the anomalies of gravity at 

 each station except upon the Pratt-Hayford hypothesis. We are 

 thus thrown back upon those earlier studies which deal with 

 deflection of the vertical. 



hayford's fundamental assumption concerning the distribu- 

 tion OF MASS WITHIN THE EARTH'S SURFACE-SHELL 



Lack of knowledge concerning distribution of mass beneath the 

 earth's surface. — If we assume, as Hayford has done in conformity 

 with the usual conception, that the differences between geodetic 

 and astronomic locations of station are a measure of the horizontal 

 components of the earth's gravitation at the station, these differ- 

 ences must be assumed to be made up of the horizontal components 

 of the pulls from all elementary volumes of the earth when multi- 

 plied by mass and divided by the square of the distance from the 

 station. But next to nothing is known concerning the distribution 

 of density within the lithosphere. As Gilbert has said, "The inner 

 earth is the inalienable playground of the imagination." 

 • * By Bowie alone. 



