THE THEORY OF ISOSTASY 



607 



sea feveJ 



may be taken as a measure of the degree of incompleteness of com- 

 pensation." 1 In order to make this idea exact, let A and B (Fig. 1) 

 represent two columns each of horizontal cross-section, a, and 

 extending to the depth of compensation, h I} the upper surface of A 

 being h miles above sea level and 

 the upper surface of B being at sea 

 level. Let the weight of A equal 

 W a and the weight of B equal Wb- 

 If there were no isostatic compensa- 

 tion, and if the densities of A and B 

 were the same at similar depths, then 

 W a would be in excess of Wb by the 

 amount a&h, where 8 is the mean 

 surface density of the earth. If this 

 excess of weight were entirely made 

 up for by a deficiency of density 

 below, compensation would be com- 

 plete. Therefore let the " degree of 

 completeness of isostatic compensation 

 defined as 



(Wa-Wb) 



h, 



for any segment, A, be 



M = 



aSh 



The quantity in parenthesis is the amount by which the weight of A 

 is in excess of the weight of B. The whole numerator is, therefore, 

 the weight which has been made up for by a deficiency of density 

 below the surface and the entire fraction is a number expressing the 

 part of the weight, a&h, which has been made up for. The above 

 formula holds equally well for land and ocean areas if h be taken 

 positive above sea level and negative below. 



FOR LAND AREAS 



1. If 



2. If 



3. If Wa 



4. If Wa 



Wa < Wb then M > 1 

 Wa = Wb thenM=i 

 Wb = a8h then M = o 

 WB>a8h then M<o 



1 The Figure of the Earth and Isostasy, IQC9, p. 67. 



