THE THEORY OF ISOSTASY 609 



nizing this fact Hayford set out to make a series of least square 

 solutions assuming various kinds of isostatic compensation. He 

 calculated what the deflections should be assuming isostatic 

 compensation by the use of a reduction factor, that is, a factor 

 which when multiplied by the topographic deflection will give the 

 deflection, isostatic compensation considered. In all of his solu- 

 tions Hayford assumed the isostatic compensation to be complete. 

 In his five principle solutions he assumed a uniform distribution of 

 compensation and assumed depths of compensation varying from 

 zero to infinity. 1 On these assumptions the conclusion was reached 

 that the most probable depth of compensation is 76 miles since 

 the sum of the squares of the residuals was least for this depth. 



Subsidiary solutions were made assuming (1) that the compen- 

 sation is uniformly distributed in a ten-mile substratum, (2) that 

 the compensation is greatest at the surface and decreases uniformly 

 with respect to depth until it becomes zero at the depth of compen- 

 sation, and (3) that the compensation is distributed according to 

 the law postulated by Chamberlin. 2 The method used in each of 

 these three cases was to find the depth for which the reduction 

 factor was most like the reduction factor for the most probable 

 solution assuming a uniform distribution. Hayford concluded 

 that so far as the geodetic evidence available could test them, any 

 of the three distributions of compensation postulated is as probable 

 as a uniform distribution. The depth of compensation found for 

 a distribution in a ten-mile substratum was 40 miles; for a uni- 

 formly varying distribution, 117 miles; and for the Chamberlin 

 distribution of compensation, 193 miles. 



A further interesting phase of Hayford's work is his C-solution 3 

 which was made on the assumption that there is no isostatic com- 

 pensation under land areas but that there is complete isostatic 



1 The condition that the depth of compensation is infinite is taken as equivalent 

 to no isostatic compensation. The condition that the depth of compensation is zero 

 is taken as equivalent to the condition that the topographic features do not affect the 

 plumb bob. 



3 This law postulates a maximum density difference slightly below the surface. 

 This density difference decreases rapidly at first and then more gradually with respect 

 to depth. 



3 P. 168 of iQog report. 



