Mat 15, 1914] 



SCIENCE 



701 



would be no tendency toward a rearrangement of 

 masses. 



If the heterogeneous material composing the 

 earth were not arranged in this manner at the out- 

 set, the stresses produced by gravity would tend to 

 bring about such an arrangement; but as the ma- 

 terial is not a perfect fluid, as it possesses consid- 

 erable viscosity, at least near the surface, the 

 rearrangement will be imperfect. In the partial 

 rearrangement some stresses will still remain, dif- 

 ferent portions of the same horizontal stratum 

 may have somewhat different densities, and the 

 actual surface of the earth will be a slight depar- 

 ture from the ellipsoid of revolution in the sense 

 that above each region of deficient density there 

 will be a bulge or bump on the ellipsoid, and above 

 each region of excessive density there will be a 

 hollow, relatively speaking. The bumps on this 

 supposed earth will be the mountains, the plateaus, 

 the continents; and the hollows will be the oceans. 

 The excess of material represented by that portion 

 of the continent which is above sea-level will be 

 compensated for by a defect of density in the 

 underlying material. The continents will be 

 floated, so to speak, because they are composed of 

 relatively light material; and, similarly, the floor 

 of the ocean will, on this supposed earth, be de- 

 pressed because it is composed of unusually dense 

 material. This particular condition of approxi- 

 mate equilibrium has been given the name isostasy. 



The adjustment of the material toward this con- 

 dition, which is produced in nature by the stresses 

 due to gravity, may be called the isosiatic adjust- 

 ment. 



The compensation of the excess of matter at the 

 surface (continents) by the defect of density be- 

 low, and of surface defect of matter (oceans) by 

 excess of density below, may be called the isostatio 

 compensation. 



Let the depth within which the isostatic compen- 

 sation is complete be called the depth of compen- 

 sation. At and below this depth the condition as to 

 stress of any element of mass is isostatic; that is, 

 any element of mass is subject to equal pressures 

 from all directions as if it were a portion of a per- 

 fect fluid. Above this depth, on the other hand, 

 each element of mass is subject in general to dif- 

 ferent pressures in different directions — to stresses 

 which tend to distort and to move it. 



In terms of masses, densities and volumes, the 

 conditions above the depth of compensation may be 

 expressed as follows: The mass in any prismatic 

 column which has for its base a unit area of the 

 horizontal surface which lies at the depth of com- 



pensation, for its edges vertical lines (lines of 

 gravity) and for its upper limit the actual irregu- 

 lar surface of the earth (or the sea surface if the 

 area in question is beneath the ocean) is the same 

 as the mass in any other similar prismatic column 

 having any other unit area of the same surface for 

 its base. To make the illustration concrete, if the 

 depth of compensation is 114 kilometers below sea 

 level, any column extending down below sea level 

 and having one square kilometer for its base 

 has the same mass as any other such column. One 

 such column, located under a mountainous region, 

 may be three kilometers longer than another lo- 

 cated under the sea coast. On the other hand, the 

 solid portions of such a column under one of the 

 deep parts of the ocean may be 5 kilometers 

 shorter than the column at the coast. Yet, if iso- 

 static compensation is complete at the depth of 

 114 kilometers, all three of these columns have the 

 same mass. The water above the suboceanie col- 

 umn is understood to be included in this mass. 

 The masses being equal and the lengths of the col- 

 umns different, it follows that the mean density of 

 the column beneath the mountainous region is three 

 parts in 114 less than the mean density of the col- 

 umn under the sea coast. So, also, the mean den- 

 sity of the solid portion of the suboceanie column 

 must be greater than the mean density of the sea- 

 coast column, the excess being somewhat less than 

 five parts in 114 on account of the sea water being; 

 virtually a part of the column. 



This relation of the masses in various columns, 

 and consequently of the densities, follows from the 

 requirement of the definition of the expression 

 "depth of compensation," that, at that depth, 

 each element of mass is subject to equal pressure 

 from all directions. In order that this may be 

 true the vertical pressures, due to gravity, on the 

 various units of area at that depth must be the 

 same. 



If this condition of equal pressure, that is of 

 equal superimposed masses, is fully satisfied at a 

 given depth the compensation is said to be com- 

 plete at that depth. If there is a variation from 

 equality of superimposed masses the differences 

 may be taken as a measure of the degree of in- 

 completeness of the compensation. 



The investigations of the deflections and 

 of gravity referred to seem to prove rather 

 conclusively that in the United States a con- 

 dition of isostasy exists. How perfect it 

 may be, and what is the area of the cross- 



