OF THE EABTH's AXIS OF FIGTJKE. 41 



14. The conclusions to which the investigation leads may then 

 be summed up thus : — 



(1) That the displacement of the earth's axis of figure from the axis 

 of rotation that would be effected by the elevations and depressions 

 of the kind suggested would be less than 10' of angle. 



(2) That a displacement of as much as 10° or 15° could be effected 

 by elevations and depressions of the kind suggested only if their 

 heights and depths exceeded by many times the heights of the highest 

 mountains. 



(3) That under no circumstances could a displacement of 20° be 

 effected by a transfer of matter of less amount than about a sixth 

 part of the whole equatorial bulge. 



(4) That even if a transfer of this enormous amount of matter 

 were to take place, it would not of necessity produce any effect, and 

 might only produce a small effect on the position of the axis of 

 figure. 



(5) That if by any means a considerable deviation were effected 

 of the axis of figure from the axis of rotation, enormous tidal motions 

 of the ocean would be produced, and its waters would sweep over the 

 continents much as a rising tide sweeps over a low bank on a level 

 shore. 



Postscript. 



15. It will be observed that in the extract (p.35) it is suggested that 

 the earth's axis of figure deviates in the first place by 15° or 20° 

 from the axis of rotation, and that then the two axes eventually come 

 into coincidence. It may be well, with a view to rendering the 

 discussion more complete, to add a few remarks on this point. 



16. In the case of a rigid body turning round an axis not coinciding 

 with the axis of figure there is no tendency, so far as the mere fact 

 of rotation goes, to bring the two axes together. Thus, in the dia- 

 gram, the half angle of the cone (C'Oz) would continue constant 

 when the separation of the axes had once been effected, unless ex- 

 ternal forces were brought to bear upon the body. Undoubtedly 

 cases might be specified in which the final result of the long-con- 

 tinued action of comparatively small forces would be to continually 

 diminish the angle C'Oz, and at length cause the rotation to take 

 place round the axis of figure in its new position within the body *. 

 Assuming that such forces, though very slow in their operation, are 

 actually called into play in the case of the earth, it might, of course, 

 follow that, if the axis of figure of the earth were slowly displaced 

 from its present position, the axis of rotation would follow it, and 

 thus, though the two would never get far apart, a considerable geo- 

 graphical displacement might at length be effected in the position of 

 the pole. Now the reasoning and the results arrived at in the above 

 paper have a very direct bearing on this hypothesis ; for it will be 

 observed that they serve to determine the amount and direction of 

 each of the small displacements ; and the final position of the axis of 

 figure and therefore, by hypothesis, of the axis of rotation, is the 



* One such case is mentioned in Kouth's ' Eigid Dynamics,' p. 432, 3rd ed. 



