326 Status of the Theory of Isostasy. 



Fourth, let the assumption be adopted that the com- 

 pensation extends to a greater depth than in the uni- 

 formly decreasing manner. T. C. Chamberlin proposed 

 this as a solution which seemed equally or more probable 

 to him than that which postulated uniformly distributed 

 compensation. 29 Hayford accordingly solved the abscis- 

 sas of a curve of the character suggested by Chamberlin, 

 the requirements of the solution being that the distribu- 

 tion of the compensation must satisfy the deflection data 

 as well as the other solutions. He thus gave Chamber- 

 lin 's qualitative suggestion quantitative expression. A 

 first trial solution made the limiting depth 141-3 miles, 

 a second made it 201-5 miles, and a third and closest ap- 

 proximation gave 178-6 miles as shown in curve D, 

 figure 5. 30 



These four equally probable solutions, A, B, C, D, 

 figure 5, show, in the order given, increasingly great 

 depths for the limit of isostastic compensation. 

 This increase shown is the basis for MacMillan's 

 sweeping statement "that with a slight modifica- 

 tion of the hypothesis the 'depth of compensation' 

 could be made to retreat to the center of the earth or 

 even to vanish altogether.'' It appears, for example, 

 that the assumption might be made that the compensa- 

 tion extends to a depth of 1,000 miles before it vanishes, 

 and a curve calculated to fit the assumption. The ques- 

 tion to be asked, however, is, if such an assumption has 

 any geological application or if it would be as unreal as 

 an algebraic solution leading to an imaginary root. As 

 a test of the nature of the distribution of the compensa- 

 tion under hypotheses A, B, C, and D, let the propor- 

 tion above 32 miles and the proportion above the center 

 of gravity of each solution be determined. These ratios 

 are tabulated as follows : 



Hypotheses of isostatic compensation showmg comparative dis- 

 tribution. 



A. Compensation confined to a 10 mile stratum. 



B. Compensation uniformly distributed. 



C. Compensation uniformly decreasing. 



D. Type of compensation extending to great depth. 



29 Jour. Geology, 15, 75-78, 1907. 



30 J. F. Hayford, op. cit., pp. 159-163. 



