6i 4 HARMON LEWIS 



JCfc- 

 8 x c 



i(ht+h) 



Wa — a I &idz is the weight 1 which the column A would have if its 



density were the same as in column B and is therefore equal to the 

 weight of B plus the weight which the material in A above sea 

 level would have if there were no isostatic compensation. Thus 



W A -a I 8 I dz = WB+a8h 



M= 

 or 



J(/z,- 



Jtfe- 



J (Ax 

 8i£ 



or 



W A -WB = a8h+a \ 8,dz (2) 



Substituting (2) in (1), 



a&h— { aSh-\-a I 8^2 



SAM= - I Srffe (3) 





The case of a uniformly distributed compensation will be con- 

 sidered. In this case, o\ being a constant, (3) reduces to 



8hM=-8 1 (h 1 +h) (4) 



As stated before Hay ford only considers the case where M=i. 

 He further makes the approximation of neglecting h in comparison 

 with h-,. This approximation which is permissible for depths of 

 compensation considered by Hayford but which would not be 

 allowable for shallow depths is discussed later. The relation cor- 

 responding to (4) which Hayford uses is $h=—<!> I h l . If however 

 the unknown quantity, M, is retained, the corresponding reduc- 

 tion factor which we will call F M is as follows: 



Fm =i-m — '^ v ':™ . (5) 



1 As 5 t may vary with the depth it is necessary to sum up the product of d t and 

 the small elements of depth rather than use the product, d^hi+h). 



