THE STRENGTH OF THE EARTH'S CRUST 299 



of completeness of compensation is the highest in the United States. 



On the basis of the figures for the whole United States Hayford 

 writes: "The average elevation above mean sea-level being about 

 2,500 feet, this average departure of less than one-tenth from com- 

 plete compensation corresponds to excesses or deficiencies of mass 

 represented by a stratum only 250 feet (76 meters) thick on an 

 average."^ It is this last statement, interpreting the deflection in 

 terms of mass, which has meaning to the geologist. It has been 

 widely quoted as perhaps the chief geologic result of the work and 

 yet the writer believes that it is without basis. By an oversight of 

 the author he misinterprets his results. If the present writer is 

 correct in making this statement it should not be taken, however, as 

 a criticism of the mathematical portion of the work. 



The sea-level is from the standpoint of the problem of isostatic 

 compensation but little more than a datum surface. Imagine the 

 ocean water to be converted into rock of density 2 . 7 of the same 

 mass as the water and resting on the present ocean bottom. Every 

 thousand feet of water would be replaced by 380 ft. of rock. Then 

 the sea-level surface after this transmutation is seen to lose all real 

 significance.^ To show the fallacy of taking this level as a basis for 

 interpreting the departures from compensation in terms of thick- 

 nesses, let attention be given to groups i, 2, 3, 4, 6, 11, ^ which cover 

 the United States east of the Mississippi River. The average 

 departure of these from compensation is o. 1 1 , which on the basis of 

 Hayford's statement means that the surface on the average departs 

 but 275 ft. from the level which would give complete isostatic 

 equilibrium on the hypothesis of uniform distribution of compensa- 

 tion to a depth of 122 km. If, however, this eastern third of the 

 United States be regarded by itself, its average elevation may be 

 assumed as 1,000 ft. (it is probably less). By the same reasoning as 

 Hayford applied to the whole United States, 11 per cent of this is 

 no ft. Therefore although the average deflections are slightly 



^1909, p. 59. 



^ More accurately, the equivalent rock should be imagined as suspended at the 

 mean depth of the water, but the effect of the difference in level is negligible upon the 

 topographic deflection. 



3 1909, p. 59. 



