1908] THE PHYSICS OF THE EARTH. 191 



" To imagine a mechanical substitute for the earth's constitution, without 

 the introduction of pressure, suppose an alloy of adamant to give the 

 material at the centre of such a globe, of the same size but devoid of gravi- 

 tation, a hardness three times that of armor plate. The outer layers as we 

 approach the surface must then be supposed softer and softer, until it is like 

 armor plate at a little over 0.6 from the center, and finally a very stiff fluid 

 near the surface. In addition to this arrangement of its effective internal 

 rigidity the actual earth is enclosed in a spheroidal shell of solid rock 

 analogous to granite. One can easily see that tidal forces applied to all the 

 particles of such an artificial armored sphere would produce but very slight 

 deformation, because of the enormous effective rigidity of the nucleus. 



" The principal uncertainty in this result arises from the admissible 

 variations in the assumed Laplacean distribution of density within the earth. 

 Both Radau and Darwin (cf. Monthly Notices, Roy. Astron. Soc, December, 

 1899) have pointed out that considerable variations in the internal distribu- 

 tion of density are possible without invalidating the well-known argument 

 drawn from the phenomenon of the precession of the equinoxes ; yet on 

 physical grounds it seems clear that pressure is the principal cause of the 

 increase of density towards the earth's centre. And since this does not vary 

 greatly for moderate changes in the law of density, the principle of con- 

 tinuity shows that the actual law of density within the earth cannot depart 

 very w'idely from that of Laplace. The above value of the theoretical rigidity 

 of the earth may therefore be taken as essentially accurate, and I think no 

 doubt can remain that the rigidity of our earth as a whole considerably 

 exceeds that of steel. The original conclusions of Kelvin and Darwin are 

 therefore confirmed by the present dynamical considerations based upon the 

 theory of universal gravitation." 



In this connection we should remember that the experimental 

 rigidity of steel is 808.000 and of glass 235,000 atmospheres. The 

 calculated rigidity of all the matter within the globe, found by con- 

 sidering not only all the layers, but also the density in each layer. 

 is found to be 1,028.702 atmospheres. Xow the average rigidity 

 must be greater than 750,000, because the stiffness of the crust and 

 increase of viscosity downward is neglected in the gravitational 

 method. In fact this method is not applicable to the outermost 

 layers, because the pressure there is much less than the rigidity, and 

 only becomes equal to the rigidity at a depth of something like one 

 tenth of the radius, where the pressure is 320,295 atmospheres. 



According to the experiments of Milne and Gray the rigidity of 

 granite is about one sixth that of steel ; and as steel has a rigidity 

 of 808,000 atmospheres, that of granite is about 135,000 atmospheres, 

 or a little more than one half that of glass. We may therefore take 



