230 Lord Kelvin on the Production of 



thoroughly the character of the motion of the solid throughout 

 the whole infinite space around the vibrating rigid globe. 

 They show displacements and motions of points of which the 

 equilibrium positions are in the equatorial plane, in the cone 

 of 45° latitude, and in the axial line. Fig. 2 represents 

 displacements at an instant when the globe is moving right- 

 wards through its middle position. Fig. 1 shows displace- 

 ments at an instant when the globe is at the end of its rightward 

 motion. Each figure shows also the orbit of a single particle 

 of which the equilibrium position is in the 45° cone, at a 

 distance %q from the centre of the globe. It is interesting to 

 see illustrated in fig. 1 how the axial motion is gradually 

 reduced from ±h at the surface of the globe to a very small 

 range at distance q from the surface, or 2q from the centre, 

 and we are helped to understand its gradual approximation to 

 zero at greater and greater distances by the little auxiliary 

 diagrams annexed, in which are shown by ordinates the 

 magnitudes of the axial displacements at the two chosen 

 times. 



§ 23. The gradual transition from motion h sin at parallel 

 to the axis at the surface of the globe, to motion 



— k — h sin 6 sin cot 

 2 r 



at great distances from the globe in any direction, is inter- 

 estingly illustrated by the conal representations in the two 

 diagrams for the case 0=45°. It should be remarked that in 

 reality h ought to be a small fraction of q, the radius of the 

 globe, practically not more than j^q, in order that the strains 

 may be within the limits of elasticity of the most elastic solid, 

 and that the law of simple proportionality of stresses to strains 

 (Hooke's Ut tensio sic vis) may be approximately true. In 

 the diagram we have taken h = ^q-, but if we imagine every 

 displacement reduced to £$ of the amount shown, and in the 

 direction actually shown, we have a true, highly approximate 

 representation of the actual motions, which would be so small 

 as to be barely perceptible to the eye, for a globe of 6 cms. 

 diameter. 



§ 24. Return now to our solution (53), (54), (55), (56) for 

 arbitrary or periodic motion of a rigid globe embedded in an 

 isotropic elastic solid of finite resistance to compression and 

 finite rigidity. For distances from the globe very great in 

 comparison with q, its radius, that is to say for q/r very small, 

 (55) and (56) become 



