academy 0F sciences] DISCUSSIONS OF ISOSTASY 215 



be in equilibrium. If the earth were a smooth rotating spheroid of similar constitution, gravity 

 would have its maximum value to the two poles and would decrease slowly and systematically 

 to a minimum around the Equator, and perfect equilibrium would still prevail. But the actual 

 earth is a rotating spheroid, the surface of which is not level; it rises in continents and mountain 

 ranges, and it sinks in ocean basins and deeps; and although the density and temperature of 

 the interior "shells" probably increase rather systematically toward the center, it is not known 

 that the composition, density, and temperature in each concentric shell are uniform or that 

 the pressure exerted by any one shell on the next interior shell is everywhere the same. The 

 outermost shell in particular, having an irregular exterior surface and being known to vary some- 

 what in composition and in vertical temperature gradient as well as in surface temperature, 

 departs from the conditions just assumed on an ideal spheroid. 



Hence in the actual earth various departures from a systematic latitude variation of 

 gravity on the surface and from a gravitative equilibrium in the interior may be expected. 

 If the shell strength be very great, as in a rigid earth, each shell might have large variations of 

 density from part to part, as dependent on variations of composition and of temperature, and 

 the departures from equilibrium might be large. Great differences of level could occur at the 

 surface of such an earth, and gravity would vary not only with latitude and surface altitude but 

 also with variations in the density of the crustal and deeper rocks. On the other hand, if shell 

 strength be small, as in a viscous crust resting in a fluid interior, the materials of the earth 

 would tend to arrange themselves so as to develop a uniform distribution of density in each 

 concentric shell, and all the shells would tend to acquire level surfaces, except that the outer- 

 most shell or crust might have an uneven surface if it were made of light rocks in its higher parts 

 and of denser rocks in its lower parts. 



Now the geodetic surveys of various nations have had to consider the hypothetical questions 

 above intimated in connection with the accurate determination of an ideal sea-level earth or 

 geoid, above which the actual surface of the lands rises in continents with their plateaus and 

 mountain ranges, and below which the ocean floor sinks in its basins and deeps; for it is the 

 surface of this geoid that is projected in maps and charts, and it is with reference to the geoid 

 surface that heights of lands and depths of oceans are measured. Evidently, if the earth's 

 surface were everywhere level, thus making the geoid actual, the departure of such an earth 

 from a sphere could be determined by measuring the force of gravity at many points of known 

 latitude along various meridians; for, as above noted, gravity on a spheroid should have its 

 maximum at the poles and should thence decrease systematically according to the eccentricity 

 of the spheroid to the Equator. Were it possible to increase the precision of gravity measures 

 on a vessel at sea by the barometric devices already available, the number of such measures 

 that could be made in a single year would furnish a more accurate value of the shape of the 

 earth than has been obtained from all geodetic work thus far accomplished on the continents. 

 And as it is possible, even on the actual earth, to reduce observations of gravity made by means 

 of a pendulum at various positions on the uneven lands to the value that they would have at 

 sea level in the same latitude, "gravity determinations furnish the most powerful, the most 

 accurate, known method of measuring the flattening of the earth." 2 



It is in connection with the reduction of gravity from any given altitude on land to its 

 sea-level value that the consideration of the density of the earth's crust is involved; and thus 

 geodesy is concerned with the question whether the density of the crust varies inversely with 

 its thickness, as is postulated in the theory of isostasy. For example, if gravity could be 

 measured in a balloon at a height of 2 or 4 miles, it would there be less than at sea level by a 

 small fraction, because of the increased distance from the earth's center. Hence in such a 

 case reduction to sea level would involve the addition of a small correction dependent on the 

 height at which the gravity measures were made. Similarly, on a 2-mile plateau surface or on 

 a 4-mile mountain top gravity should again be less because of altitude, but not so much less 

 as before because of the attraction of the plateau or mountain mass. It is therefore necessary, 

 in calculating the correction by which gravity at a high-level station may be reduced to its 



J J. F. Hayofrd. The importance of gravity observations at sea on the Pacific. Proc. Nat. Acad. Sci., ii, 1916, 394-398; see p/395. 



