190S] 



on the Figure, and Constitution of the Earth. 



08 



verified by observation, as the result that there is polar flattening. 

 The inequality is named eUiiMcity of the meridians. 



The existence of this inequality has often been supposed to prove 

 that the interior of the earth is fluid, or that, if not fluid now, it was 

 so once. The actual amount of the inequality, as specified by the 

 excess of the equatorial diameters above the polar diameter, is about 

 26 miles. Newton computed it on the hypothesis that the earth is 

 composed of homogeneous incompressible fiuid, and found that with 

 that constitution the amount of the inequality would be about 

 38 miles. Many years ago, Lord Kelvin pointed out that the earth 

 would have elliptic meridians if the matter of which it is composed 

 were as rigid as steel, and he showed that, if the substance were homo- 

 geneous and incompressible, and had this degree of rigidity, the 

 amount of the inequality would be about 11 miles. [The numbers 

 were thrown on the screen.] As the substance is neither homo- 

 geneous nor incompressible, these results do not decide the question 

 of internal fluidity. 8o far it has not been possible to take account 

 theoretically of the compressibiUty or of the heterogeneity, but it is 

 probable that both would increase the computed ellipticity. If this 

 could be proved, the actual amount of the inequality would show 

 that the interior of the earth has a high degree of rigidity. 



Rigidity of a substance may be defined qualitatively as capacity to 

 stand in a shape, or in a state, which requires the existence, within 

 the substance, of difi^erent pressures in different directions. There is 

 a corresponding quantitative definition in terms of the amount of force 

 required to produce a given change of shape. 



This table [thrown on the screen] shows the rigidities of some sub- 

 stances, steel being regarded as a standard. The last entry in the 

 table is the average rigidity of the materials of the earth, as deter- 

 mined by the rate of transmission of earthquake shocks to great dis- 

 tances. The conclusion that the earth is a very rigid body was 

 reached by Lord Kelvin, by investigations on the tides, and by Sir 

 George Darwin, by investigations concerning the stress produced in 

 the interior by the weight of continents and mountains, and it has 

 been confirmed in a very striking way by recent investigations in 



