18G SEE— FURTHER RESEARCHES ON [April 24, 



Eulerian Precession," read to the Cambridge Philosophical Society, 

 May 25, 1896, Professor Lannor showed how to estimate the effect of 

 the elastic yielding of a rotating solid on the period and character 

 of the free precession of its axis of rotation, and again confirmed 

 the high effective rigidity of the earth from another point of view. 



The observed prolongation of the Eulerian period is thus fully 

 explained by the imperfect rigidity of the earth's mass, and the 

 high rigidity thus deduced has naturally strengthened the earlier 

 conclusions of Kelvin and Darwin drawn from the study of the 

 long period tides of the sea. 



This investigation, like those already cited, gives us only an 

 average effect for the earth as a whole, but does not tell us the law 

 of the distribution of rigidity within the globe. If this law of dis- 

 tribution of rigidity could be found, even approximately, it would be 

 of great interest, because we could then see in what part of the globe 

 the principal part of the yielding takes place ; and this would give 

 us a much better understanding of the internal constitution of our 

 planet than heretofore has been considered possible. 



§ 17. Rigidity of the Earth Calculated from the Theory of 

 Graznty, on the Hypothesis that the Distribution of Rigidity in the 

 Globe is Ez'eryivhere Proportional to the Pressure. — It has not been 

 supposed by previous investigators that a method could be devised 

 for deducing the rigidity of a body like the earth from the theory 

 of gravity; but in 1905 it occurred to the present writer that such a 

 method could be found if we could adopt a suitable hypothesis for 

 the variation of the rigidity with the pressure. Previous investi- 

 gations of the internal state of the heavenly bodies had justified the 

 law of Laplace as giving an excellent approximation to the law of 

 density for the earth and the rest of the encrusted planets ; and 

 the monatomic law had been found most satisfactory for the sun 

 and fixed stars (cf. A. A'., 4053). These laws enable one to ob- 

 tain the pressure at every point of the radius of the heavenly bodies. 

 For in several ways Laplace's law of density is fairly well estab- 

 lished for the earth, and on equally good grounds the density of the 

 sun is believed to conform essentially to the monatomic law. 



From a study of the laws of density, pressure and temperature 

 within the heavenly bodies it appeared to me (as it had indepen- 



