1896.] Earth's Free Eiderian Precession. 193 



surface ; which finally heals up after the surrounding stress is 

 reduced in the main to hydrostatic pressure. 



15. It has been estimated by Mr Hough 1 that, were the 

 Earth a homogeneous solid with the actual surface ellipticity, the 

 Chandler period for the free precession would require that it 

 should have the rigidity of steel. The order of magnitude of 

 this result will not be entirely altered by actual heterogeneity : so 

 that, if we can assume the correctness of this period, we may 

 conclude that, as regards the slight stresses here involved, the 

 Earth is an elastic solid of about the same order of rigidity as 

 steel. This is in fair accord with the observations of seismologists 3 , 

 who find that earthquake shocks are propagated to distant parts 

 of the Earth not only by the ordinary surface waves, but also by 

 minute tremors which enormously outrun the earthquake proper, 

 arriving in a time that would correspond to propagation in a 

 straight line across the interior of the Earth, provided it possessed 

 an average rigidity about § of that of steel. 



(4) Note on a point in theoretical dynamics. By Sir 

 Robert Ball. 



Let a be a screw about which a free rigid body is made to 

 twist in consequence of an impulsive wrench administered on some 

 other screw ij. Except in the case where a and rj are reciprocal it 

 will always be possible (in many different ways) to design and 

 place a rigid body so that two arbitrarily chosen screws a and rj 

 will possess the required relation. 



Let now /3 and f be two other screws (not reciprocal) ; we may 

 consider the question as to whether a rigid body can be designed 

 and placed so that a shall be the instantaneous screw correspond- 

 ing to ?; as an impulsive screw while /3 bears the same relation 

 to £. 



It is easy to see that it will not generally be possible for a, /3, 

 7], f to stand in the required relations. For taking a and /3 as 

 given there are five disposable quantities in the choice of n and five 

 more in the choice of £. We ought therefore to have ten dis- 

 posable coordinates for the designing and the placing of the rigid 

 body. But there are not so many. We have three for the co- 

 ordinates of its centre of gravity, three for the directions of its 

 principal axes, and three more for the radii of gyration. The mass 

 of the body is not disposable. The other nine quantities being 

 assigned the relations of the impulsive and instantaneous screws, as 



1 Loc. cit. Phil. Tram., 1896. 



- Cf. Prof. Milne, Brit. Assoc. Report, 1896, "On Earthquake Phenomena." 



