1896.] Earth's Free Eulerian Precession. 187 



direction ; which is in agreement with the accepted doctrine that 

 the Earth assumed originally a form of fluid equilibrium, in which 

 it has been gradually solidifying, so that were the centrifugal 

 force now removed it would still retain an oblate form. 



6. The practical outcome, as regards Astronomy, is that, as 

 the precessional constant (G — A)/C of the actual Earth is deter- 

 mined precisely by the periods of the ordinary astronomical 

 precessions and nutations, so also the modified precessional 

 constant (C" — A')/ A' of the Earth as it would be were the centri- 

 fugal force of the axial rotation removed, can be estimated from 

 the period of the free Eulerian precession, — in so far, that is, as 

 this period can be disentangled from the actual observations of 

 changes of latitude, which are also affected by large irregular 

 variations due to meteorological causes, and more or less of an 

 annual character. As the value of G — A is determined by a 

 knowledge of the variation of gravity at the Earth's surface, the 

 values of G and A are separately known; and therefore the value 

 of G' — A' is approximately known in terms of the Eulerian period, 

 thus affording an additional datum of somewhat precise character 

 for investigations relating to the physical condition of the Earth's 

 interior. 



On the other hand, the forced nutations due to extraneous 

 astronomical forcives, even those of short period, are of course 

 not sensibly affected by the circumstance that the centrifugal 

 part of the Earth's ellipticity follows the movements of the axis 

 of rotation. 



7. The conclusions above stated are restricted to the case of 

 a solid body, that is, one in which parts which were initially near 

 together cannot wander far apart during the motion. If a large 

 portion of the interior is fluid, other considerations will influence 

 the result 1 . If the interior of the Earth were all fluid except an 

 enclosing shell of moderate thickness, say a few hundred miles, 

 there could be no sensible free steady precession at all, unless the 

 rigidity of this shell were far beyond any that is actually known. 



The slight change of configuration due to transfer of the 

 centrifugal force to a new axis of rotation, which is here contem- 

 plated, need not be purely elastic, in order to make the conclusions 

 valid. It may be in part viscous : but the wide discrepancy 

 between the actual period of the Earth's free precession and the 

 one that would apply to a perfectly rigid Earth is evidence that 

 this deformation is really in large part elastic. For if elasticity 

 proportional to, or a function of, strain were entirely absent, then 



1 Cf. Kelvin, Math, and Phys, Papers, Vol. in. p. 132; Hough, Phil. Tram, 1895. 



