332 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 31 



pensation is very irregular and that crustal masses under the con- 

 tinents extend much farther below sea level than do such masses 

 under the oceans. Under mountain areas these protuberances would 

 be greater than under plateaus and valleys. 



We have not yet been able to prove which of the two hypotheses 

 is the true one, since the application of either of them to gravity and 

 deflection data gives about the same satisfactory results. However, 

 looking at the matter from a purely physical standpoint, I am in- 

 clined to think that there are decided weaknesses in the Airy hy- 

 pothesis and that the Pratt hypothesis is probably the true one. 

 Perhaps with a greater accumulation of data we may in the future 

 be able to show which one of these hypotheses is the better one. We 

 should be able to derive a depth of compensation for each extensive 

 mountain area and if the Airy hypothesis is the true one, then the 

 higher the mountain area the greater should be the derived depth 

 of compensation. When such mountain areas as the Andes and the 

 Himalayas are covered by geodetic stations, it should be possible 

 to make this test. 



ASSUMPTIONS UNDERLYING ISOSTATIC INVESTIGATIONS 



Xecessaril}^, in carrying on such investigations as have been in- 

 volved in the tests of isostasy, assumptions have to be made. The 

 assumptions made by geodesists are approximately as follows : First, 

 that isostasy is complete or perfect for even quite limited portions 

 of the earth's crust; second, that there is a uniform distribution with 

 respect to depth of the compensating deficiencies of density under 

 continents and of the excesses of densities under oceans, that is, that 

 the compensation starts at sea level and extends uniformly about CO 

 miles to the lower limit of the crust; third, that the cosnpensation 

 is directl}^ under the topographic feature and not spread out hori- 

 zontally with respect to that feature; and fourth, that the density 

 of the rock above sea level is 2.67. 



These assumptions are made merely for the convenience of the 

 investigator. It would be practically impossible for him to assume 

 anj^thing but very simple conditions because of the very large amomit 

 of work involved in making the computations required for the tests. 

 We do find that, when these assumptions are made and corresponding 

 corrections are computed, the theoretical and actual values for the 

 astronomical longitudes and latitudes and for values of gravity are 

 brought very closely into agreement. There are some outstanding 

 differences, and these must be a measure of the degree to which one or 

 more of the assumed conditions are not true. The lower limit of 

 compensation may not be a regular surface, it may be very much 

 deeper under some parts of the continent than under others, and it 



