,907] AND CONTRACTION OF THE EARTH. 199 



law of compressibility of the matter, of which before its consolida- 

 tion the earth consisted, was that the increase of the square of the 

 density is proportional to the increase of the pressure, or dp = Kcrdcr, 

 the integrating of which gives (cf. A. N., 3992) 



o- ^ e^m^) ^ <7p sin {^x) 

 X ^^ ' 



When calculated numerically the density, pressure and theoretical 

 effective rigidity are found to be as given in the foregoing table 

 (cf. A. N., 3992, 4104). 



The hypothesis employed in deducing the rigidity of the earth 

 and other heavenly bodies, namely that the rigidity is proportional 

 to the pressure, has been discussed in A. N., 4152, as follows: 



" In ordinary solids such as the metals the property of rigidity is pro- 

 duced by the action of molecular forces which resist deformation. On the 

 other hand the matter within a planet like the earth is really gaseous but 

 above the critical temperature, and therefore in confinement made to behave 

 as an elastic solid wholly by virtue of pressure which brings the molecules 

 within distances at which they again become effective in spite of the high 

 temperature. Thus in cold solids the property of rigidity is due simply to 

 molecular forces which prevent deformation, while for gaseous matter in 

 confinement under such pressure that it acquires the property of an elastic 

 sold, the property of effective rigidity is due wholly to the pressure. In the 

 paper above cited I have therefore taken the rigidity to be directly propor- 

 tional to the pressure, and ignored all other influences, such as temperature, 

 because by hypothesis the density is assumed to follow Laplace's law, or the 

 monatomic law, in the case of purely gaseous masses, and the temperature is 

 supposed to be conformable to the laws of density. 



"This hypothesis seems legitimate, and almost certainly as accurate as 

 Laplace's law and the monatomic law, upon which the calculated pressures 

 depend. Moreover the validity of the hypothesis that the rigidity is propor- 

 tional to the pressure appears to be confirmed by the close agreement of the 

 numerical values of the earth's rigidity found in this way with those found 

 by the recognized empirical processes depending on the tides and the polar 

 motion." 



If this reasoning is justifiable, it becomes possible to calculate 

 the rigidity of the matter at any depth within the earth, and we are 

 enabled to conclude that the yielding of our globe under the influence 

 of tidal forces to which it may be subjected is mainly superficial. 

 The results of these calculations are illustrated by the curves drawn 

 in the accompanying diagram, Fig. F. 



Observations seem to prove that in transmitting earthquake waves 



