Prof. F. W. Clarke, making use of the above data, has worked out the relative abundance of the chemical elements in the combined mass of the atmosphere, the hydrosphere and the litho sphere. His results are given in the following table. (Consult Bulletin of the United States Geological Survey, No. 78). It is interesting to note that nearly one-half of that part of the mass of the earth visible to us is oxygen, the next most abundant contributions being, in or der, silicon, aluminum, iron and calcium.
The Since, the crust of the earth, as seen above, rests like a viscous fluid on the centrosphere, the latter, whatever its tem perature and other properties, must be subject to great internal stress. Indeed, the mechanics of celestial bodies of large mass leads inevitably to the conclusion that pressure is the dominant factor in the earth at no great depth below the surface. Given time enough, therefore, tribution of pressure will be essentially the same as if the mass of the earth were fluid. This justifies the application of the laws of hydro statics to the earth as a whole, whether it was originally fluid or not. With this concept, and with the law of gravitation, several facts enable us to determine within narrow limits what must be the constitution of the earth as regards dis tribution of density, gravity and pressure. The
principal of these facts are (1) the surface density, (2) the mean density, and (3) the sur face value of the acceleration of gravity. In ad dition to these facts, there are some others of less importance depending on the attraction of external bodies of the earth. Laplace correlated all these facts by means of a hypothesis with regard to the compressibility of matter. This asserts that the pressure in the earth increases as the square of the increase in density.
Adopting the indications of Laplace the fol lowing table showing the variation of density, acceleration of gravity and pressure with depth below the surface of the earth has been com puted. The relatively unimportant effect of the rotation of the earth is ignored in the calcula tion. The assumed values of the surface density and the mean density are 2.75 and 5.5, respec tively, times that of water. In the third column of the table g represents the average surface value of the acceleration.