ISOSTASY AS A WORKING HYPOTHESIS 273 



assumption of sealevel as a reference datum, the definition may stand. 

 It is then equivalent to the statement : there is a depth at which isostatic 

 compensation is complete, and this depth shall be called the depth of 

 compensation. If, however, we raise the question. Is the depth of com- 

 pensation uniform? we must answer. No, not according to geologic and 

 physical evidence. It probably ranges through several hundred miles 

 and may involve a large part of the globe. 



Is isostatic equilibrium nearly perfect, as is indicated by the geodetic 

 calculations ? Probably not, for those calculations rest on the assumption 

 of an artificial scheme of density distribution, and on assumed conditions 

 of hydrostatic pressure which can not exist, except where there is local 

 and temporary melting. 



What, then, is the significance of the figure of 76 miles, calculated by 

 Hayford, or of 60 miles, more recently published by Bowie, as the mean 

 depth of compensation ? Is there any basis for believing that it approxi- 

 mately defines the base of the isostatic shell? Even though the mathe- 

 matical demonstration is too precise, I believe there is such a basis and 

 that the general conclusion regarding isostasy is not invalidated. My 

 reasons are as f oUows : 



It is probable that heterogeneous masses in the lithosphere and nucleus 

 are of much greater horizontal dimensions than vertical dimensions. 

 Thus, a lens of basalt 10 miles thick and but 100 miles in diameter 

 would be an exceedingly thick lens. One to one hundred or one thou- 

 sand would seem more probable ratios. If this be so, we may say that 

 the lithosphere is thin bedded as to density. The number of variations 

 of density is, then, large in any column of considerable depth. 



Second, the differences of density existing between masses at or near 

 the same level in the lithosphere are relatively not great. A difference 

 of 10 per cent would be large. 



If these conditions exist in columns, say, 700 miles high, extending 

 from the base of the isostatic shell through the asthenosphere to the base 

 of the latter, it is probable, under the law of averages when applied to 

 numerous small differences, that any two columns will have nearly equal 

 average densities. The resulting inequalities of gravitative stress would 

 be correspondingly small. 



Furthermore, the mean radius of attraction of these differences, as 

 observed from points on the surface, would be 400 miles. Their effect 

 on the observations of gravity would be relatively slight. 



By contrast, similar differences of gravity occurring in the outer 100 

 miles of the crust, in the isostatic shell, would produce correspondingly 

 large anomalies of gravity. 



