WHAT IS TERRA FIRMA? WILLIS. 401 



The deflection is due to lateral attraction, which may be exercised 

 by mountain masses or by dense bodies within the earth's crust lying 

 on one side of the station, or by both sources of attraction. The in- 

 fluence of topographic features, whose masses are more or less ac- 

 curately ^determinable, can be calculated. There then remains a 

 residual attraction which is presumably due to a dense body, but 

 before accepting that conclusion it is necessary to eliminate any 

 erroneous assumption that might have a similar effect. 



Among the subsidiary investigations which Hayford made was one 

 relating to the depth below sea level at which all the columns which 

 extend downward from the earth's surface are balanced. At one 

 extreme he calculated the values of gravity on the assumption that 

 this depth, which is called the depth of compensation, is zero ; that is, 

 there exists immediately below every elevation the full compensating 

 defect of density and below every depression the full compensating 

 excess of density necessary to balance the inequalities of height. At 

 the other extreme he calculated the values of gravity on the assump- 

 tion that the depth of compensation is infinity; that is to say, the 

 earth is so rigid that there is no compensation in the finite radius. He 

 also made similar computations for intermediate depths of the level 

 of compensation. That which gave the most accordant values of 

 gravity and which is therefore regarded as most reliable was at first 

 ascertained to be 114 kilometers, but was subsequently corrected to 

 120.9 kilometers. Helmert has arrived at the value of 123 kilometers 

 by independent computations. There is, therefore, no doubt but that 

 this value commands a certain confidence under the primary assump- 

 tion of complete isostatic compensation. It may, however, be re- 

 garded as an average, from which there are in fact greater or less 

 variations in different localities, and it also depends upon the postu- 

 late that the density of each individual column remains the- same 

 from the surface to the bottom at 123 kilometers. It is more probable 

 that the density increases downward, and this would somewhat 

 modify the value of 120.9 kilometers. Nevertheless this conception 

 of a definite lower limit to the zone of compensation is of the highest 

 value. At and below that depth all pressures due to gravity are by 

 hypothesis equal. 



In calculating the topographic correction before making the vari- 

 ous computations for the depth of compensation, Hayford took ac- 

 count of all irregularities of the earth's surface to a distance of 2,564 

 miles from each station in all directions. The immense labor of these 

 computations was brought within practicable limits by special 

 methods devised to that end. As the stations ranged in position from 

 the Atlantic to the Pacific coast, the depths of the Atlantic and Pa- 

 cific basins were included among the features considered, as well as 



975TS°— SM 1910 26 



