Status of the Theory of Isostasy. 335 



It is seen that for India the deflections computed from 

 the topography alone, as listed in column D, give a sys- 

 tematic attraction of the plumb-line to the north. This 

 is due to the great elevations of the Himalaya Mountains 

 and the Tibetan plateau to the north and to the deep 

 ocean basins to the south. The plateau of India is thus 

 the middle one of three great steps in the earth's sur- 

 face. This is why the topographic deflections for most 

 of the regions are much larger than for the United States. 

 The computations on the hypothesis of complete compen- 

 sation of the topography at a depth of 113-7 kilometers 

 are given in column E and are seen to reduce the topo- 

 graphic deflections to very small quantities for all regions 

 except those adjacent to the Himalaya. This is of 

 course no proof of isostasy unless the computed deflec- 

 tions correspond to the observed deflections. The dif- 

 ferences between the observed deflections, shown in 

 column F, and the topographic deflections are given in 

 column Gr. They are a measure of the error of the 

 hypothesis of no isostasy on the assumption that the 

 Bessel-Clarke spheroid is correct. This measure of the 

 error of this hypothesis is not directly comparable with 

 the residuals for the United States of solution B, the 

 hypothesis of no isostasy, for the reason that in solution 

 B such values of the radius and polar flattening were 

 taken as made the sum of the squares of the residuals 

 smallest and these constants were appreciably different 

 from those of the Bessel-Clarke spheroid. The terres- 

 trial dimensions adopted by Hayford for the hypothesis 

 of isostasy are also different from those of the Bessel- 

 Clarke spheroid, but probably not enough to affect the 

 comparison of isostasy in the two countries. 



Column H shows the discrepancy between the observed 

 deflections and the deflections for topography fully com- 

 pensated at a depth of 113-7 kilometers. Columns G 

 and H are therefore the residuals given by the two 

 hypotheses. Their ratio, as given in column I, measures 

 their relative probabilities. Although the residuals for 

 both hypotheses are large for the Himalayan foothills, 

 it is seen that the mean for the Hayford hypothesis is 

 only one-third of the mean for no isostasy. The average 

 of the means for the other groups shows that the par- 

 ticular hypothesis of isostasy which is used gives resid- 

 uals less than a tenth as large as the hypothesis of no 

 isostasy. 



