616 HARMON LEWIS 



though the reduction factor becomes larger, the relative increase 

 in the various rings is not the same as the increase when h L is made 

 larger than 76 but M is kept equal to 1. 



On the other hand, when o<lf<i and ^!<76, the resulting 

 factor, for any given ring, compared to F for h z = 76, tends to become 

 larger on account of taking M<ii, but tends to become smaller on 

 account of taking /?!<76. If h x be taken sufficiently small, the 

 factor, Fm for M<i, and Ai<76, becomes smaller for certain rings 

 and. larger for other rings than F for 7^=76. It therefore seems 

 quite probable that a combination of M<\ and h 1 <j6 should 

 prove to be as close an approximation to the facts as M = 1 and h x = 

 76. 



Similarly, if the case where M>i were to be considered, the 

 best depth of compensation would probably turn out to be greater 

 than 76 miles. 



By equation (6) above, it is an easy matter to calculate the factor 

 Fm for any value of h x which is equal to the radius of any ring. In 

 order to obtain a typical example, the factors were calculated assum- 

 ing M= . 5 and h L = 19. 29 kilometers (11 .987 miles) and are given 

 below together with the factors for Hayford's most probable solu- 

 tion in which it was assumed that M= 1 and h x = 113 . 7 kilometers 

 (70.67 miles). 1 



It will be noted that, for outer rings, the factor, Fm , is approxi- 

 mately .5 while F is nearly zero. From the examples of calcula- 

 tions of "topographic deflections" given by Hayford it would 

 seem that the outer rings, especially the oceanic compartments, 

 have a considerable effect on the topographic deflection. It 

 might seem, therefore, that M=.$, ^=19.29 kilometers would 

 not give as close a result as M=i, 7^= 113. 7 kilometers; but 

 without some sort of test this question would remain a matter of 

 conjecture. Furthermore the additional hypothesis might be 

 introduced that the compensation under ocean areas is complete 

 or even that ocean areas are over-compensated. Then when we 

 remember that the assumption regarding either M' or h z or both may 



1 The value of the depth of compensation given in the first report as most probable 

 is 70 miles. In the second report 76 miles is given, but the reduction factors for this 

 depth are not published. 



