An approximate definition of isostasy is in dicated by the historical statement already made An exact definition is given in the few paragraphs which follow this.
If the earth were composed of homogeneous material, its figure of equilibrium, under the in fluence of gravity and its own rotation, would be an ellipsoid of revolution.
The earth is composed of heterogeneous ma terial which varies considerably in density. this heterogeneous material were so arrange that its density at any point depended simply upon the depth of that point below the sur face, or, more accurately, if ill the material lying at each equipotential surface (rotation considered) was of one density, a state of equi librium would exist and there would be no tend ency toward a rearrangement of masses. The figure of the earth in this case would be a very close approximation to an ellipsoid of revolu tion.
If the heterogeneous material composing the earth were not arranged in this manner at the outset, the stresses produced by gravity would tend to bring about such an arrangement. But as the material is not a perfect fluid, as it possesses considerable viscosity, at least near the surface, the rearrangement will be imper fect. In the partial rearrangement some stresses will still remain, different portions of the same horitontal stratumT itime what different densities, and the -actual surface of the earth will be a shed departure 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 pla teaus, the continents ; and the hollows will be the ocean. 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, similarb , the floor of the ocean, will, on this supposed earth, be depressed because it is composed of unusually dense material. This particular condition of approximate eronlibritun has been given the name isostasy.
The compensation -of the excess of matter at the surface (continents) by the defect of density below, and of surface defect of matter (oceans) by excess of density below, may be called the isostatic compensation.
Let the depth within which the isostatic com pensation is complete be called the depth of compensation. At and below this depth the condition to stress of any element of mass is isostatic; that is, any element of mas is sub ieet to equal pressures from all directions as if it were a portion of a perfect fluid. Aliove this depth, on the other hand, each element of mass is subject in general to different pressures in different directions — to stresses which tend to distort it and to move it. • In terms of masses, densities and volumes, the conditions above the depth of compensa tion 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 compensation, for its edges vertical lines (lines of gravity) and for its upper limit the actual irregular surface of the earth (or the sea surface 'if the area in ques tion is beneath the ocean) is the same as the mass in any other similar prismatic column hav ing any other unit area of the same surface for its base. To make the illustration concrete, if the depth of compensation is 76 miles below sea level, any column extending down to this depth below sea level and having one square mile for its base has the same mass as any other such column. One such column, located under a mountainous region, may be two miles longer than another located under the seacoast. On the other hand, the solid portion of such a column under one of the deep parts of the ocean may be three miles shorter than the col umn at the coast. Yet, if isostatic compensa tion is complete at the depth of .76 miles, all three of these columns have the same mass. The water above the suboceanic column 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 two parts in 76 less than the mean density of the column under the seacoast. So, also, the mean density of the solid portion of the sub oceanic column must be greater than the mean density of the seacoast column, the excess be ing somewhat • less than. threeilatte. in 76 oh :account of the sea water being virtually a part of the column.