312 Status of the Theory of Isostasy. 



assumes that the relief of the earth is neutralized by 

 compensation at the surface, in other words, that topog- 

 raphy has no influence on the deflections of the vertical. 



Instead of comparing the residuals of the several solu- 

 tions with each other, Hayford has taken the ratio of 

 the mean residual of solution H to the mean topographic 

 deflection as a test of the value of isostasy. The ratio 

 of the mean residual to the mean topographic deflection 

 might almost as well be used as a proof of the absence 

 of isostasy, since it is observed that solution B, no isos- 

 tasy, gives a mean residual for the whole United States 

 which is less than one-third of the value of the mean 

 topographic deflection. There is much less difference 

 between these residuals than there is between them and 

 the mean topographic deflection. 



The topographic deflection is not a direct measure of 

 the discrepancy due to the hypothesis of no isostasy, as 

 Hayford has here used it. There the observed deflection 

 must be subtracted algebraically from the topographic 

 deflection, and then further corrections made, due to 

 errors in the initial longitude, latitude, or azimuth, also 

 to the initial radius of the earth, and the square of the 

 eccentricity. The corrections are notable quantities 

 serving to materially change the value of the residuals. 

 They are the unknowns derived from the normal equa- 

 tions into which all the observations enter, and have a 

 different value for each hypothesis regarding isostatic 

 compensation. It is true that the value of these correc- 

 tions as given by solution B does not agree with the 

 values obtained from some other lines of evidence as 

 well as do the corrections obtained from solutions E, 

 H, or G, but that is to one side of the present argument. 



It is seen that for the eastern United States removed 

 from the seaboard, especially groups 3, 4, 5, 6, the resid- 

 uals of solutions H and G are one-half to three-quarters 

 as large as those of solution B, no isostasy. This is a 

 clear indication that irregularities of density not related 

 to topography have more influence upon the deflections 

 than the topography of the lands east of the Mississippi. 

 This feature is especially striking in the Lake Superior 

 region, group 5, but is almost as notable in the southern 

 Appalachians, group 4. In Southern California, group 

 10, many of the stations are near the coast. Here the 

 influence of the larger features of the earth is at a maxi- 



