THE THEORY OF ISOSTASY 



6i5 



Adding and substracting M, we have 



Fm=i-M(i-F) 

 where F, the reduction factor obtained by Hayford, is 



log 



F=i- 



r I -\-V'r I '+h I 2 



log 



r 1 



(6) 



(7) 



Comparing F with Fm we see that, when 0<Af<i, F M will be 

 greater than F for the same ring 1 and h x . Also for any given ring 

 F is larger, the larger the depth of compensation, 2 h T . It follows, 

 therefore, that Fm for Af<i calculated on any given h T will be 

 greater for all rings than the corresponding factor, F, calculated 

 on a smaller h I} for 



Fu 



> 



M<i 



F 



h 1 = x 



> 



F 



hi<x 



or 



F 



M 



> 



M<i 

 hz>76 



F 



h = y6 



Now assuming M= 1 Hayford has already shown that the set of 

 factors obtained when ^=76 miles gives a closer result than the 

 set of larger factors obtained when h x > 76 miles. It seems probable 

 therefore that, if a solution were to be attempted assuming 0<M 

 <i, nothing would be gained in taking a depth of compensation 

 larger than the most probable depth assuming M= 1. The writer 

 would not care to make the preceding statement as a positive 

 fact without an inspection of the data for the calculation of the 

 topographic deflections. For it seems possible, although not 

 probable, that a combination of M <i and /? x > 76 might yield as 

 close a result as M = 1 and ^1=76 on account of the fact that, 



1 In calculating the topographic deflection the area around any station is divided 

 into concentric rings whose outer radii are r 1 and inner radii, r z . 



2 See table, p. 70 of 1909 report. 



