322 Status of the Theory of Isostasy. 



Isostasy is concerned only with the differences of density 

 under different horizontal areas corresponding to their 

 differences in elevation. Small errors in the specific 

 gravity of the relief of the earth's surface give rise 

 merely to small corrections which have been discussed 

 by both Bowie and the writer. 



A critic should take the trouble to prove his criticism, 

 not leave it as a doubt to unsettle those who cannot be 

 expected to prove or disprove it. The assumption of a 

 datum at — 9,000 feet is equivalent in the problem of 

 deflections to increasing all elevations 9,000 feet. Such 

 an assumption is readily applied to the examples of 

 computations of topographic deflection. 26 The topog- 

 raphy surrounding the station is covered by a series of 

 annular zones or rings whose centers are at the station. 

 Each ring is divided into compartments. The compart- 

 ments are so taken that for a unit mass in the compart- 

 ment each has a unit effect in deflecting the vertical in 

 the plane of the meridian or prime vertical. For each 

 compartment the increase of elevation by 9,000 feet in- 

 creases the deflection 0-9", but in the sum of the compart- 

 ments of any one ring, the half on one side pull one way, 

 the half on the other side pull the other way, and it is 

 difference of masses which alone has effect. The con- 

 stant increase of 0-9" for each compartment, due to 

 change of datum, therefore cancels out. The deflection 

 due to the compensation as distinct from the topography 

 is obtained by multiplying the deflection due to topog- 

 raphy by a reduction factor which varies with the hori- 

 zontal distance from the station but does not involve the 

 elevation of the station. 27 Thus, change of datum, on 

 direct application to the illustrative problems, is observed 

 to have no effect in the result. 



The influence of change of datum upon the computa- 

 tions of gravity remains to be considered. 



Let the intensity of gravity at any station be com- 

 puted under the assumption of isostasy according to 

 Hayf ord and Bowie 's method, using the sea-level datum. 

 The mass of each unit area to be compensated is $h, in 

 which 8 is mean surface density and h the elevation. Next 

 assume a new datum, — 0, figure 4, at a depth c below 

 the initial datum. The elevation of each unit area now 



23 J. F. Hayf ord, op. eit., pp. 26-33, 1909. 

 27 J. F. Hayf ord, op. eit., pp. 68-73. 



