THE STRENGTH OF THE EARTH'S CRUST 147 



at each station, after allowing for the small errors of observation, 

 what are the deflections of the vertical produced by the variations 

 of relief and density. But this deflection for each station is the net 

 result of all the relief from mean level and all the subsurface 

 departures from the densities necessary to sustain that relief for 

 distances of hundreds and, to a diminishing extent, even thousands 

 of miles. The problem is made more soluble, however, by another 

 and independent mode of attack. Observations on the intensity of 

 gravity, when corrected for latitude, for elevation, for the sur- 

 rounding relief and the density theoretically needed to sustain that 

 relief, show the vertical component of those outstanding forces 

 whose horizontal component was measured by astronomic determi- 

 nations. It is seen that if the topography is known and its influence 

 evaluated, and sufficient observations are reduced, the distribution 

 of subcrustal densities and consequently the amount of crustal 

 strains form soluble but complex problems. 



The mathematical mode of investigation of such problems has, 

 however, both its advantages and disadvantages. The advantages 

 lie in giving quantitative results and in the test of the accuracy of 

 the trial hypotheses by means of the method of least squares. A 

 disadvantage lies in the necessity of erecting simple hypotheses in 

 place of the complex realities of nature, in order to bring the data 

 within the range of mathematical treatment. The precision of 

 mathematical analysis is furthermore likely to obscure the lack of 

 precision in the basal assumptions and through the apparent 

 finality of its results tends to hide from sight other possibilities of 

 the solution. 



It is because of the geologic nature of the hypotheses on which 

 the calculations concerning isostasy rest, and the geologic bearing 

 of the results, that it is no act of presumption for the geologist to 

 enter into this particular field of the geodesist. 



The measurements of isostasy have been placed most fully on 

 a quantitative basis by Hayford, and the science of geology is in- 

 debted to him in large measure. In the following consideration of 

 the geodetic evidence attention will be confined almost entirely to 

 his work, supplemented by that of Bowie. Hayford was the first 

 to consider the influence of the topography and its compensation 



