Elastic Solids at Best or in Motion in a Liquid. 



235 



opinion, the view I put forward in 1877 that " new stars " are produced 

 by the clash of meteor-swarms ; and they have suggested some further 

 tests of its validity. 



We may hope since observations were made at Harvard and Potsdam 

 very near the epoch of maximum brilliancy, that a subsequent complete 

 discussion of the results obtained will very largely increase our know- 

 ledge. The interesting question arises whether we may not regard the 

 changes in spectrum as indicating that the very violent intrusion of the 

 denser swarm has been followed by its dissipation, and that its passage 

 has produced movements in the sparser swarm which may eventuate in 

 a subsequent condensation. 



My best thanks are due to those I have named for assistance in this, 

 inquiry. 



" Elastic Solids at Eest or in Motion in a Liquid." By C. Cheee, 

 Sc.D., LL.D., E.K.S. Eeceived November 19, — Eead Decem- 

 ber 13, ] 900. 



§ 1. The problems dealt with in the present paper are probably of 

 little practical importance ; but they seem of considerable interest 

 from the standpoint of dynamical theory. The hard and fast line 

 which it is customary to draw between Rigid Dynamics and Elastic 

 Solids has been discarded, and a more direct insight is thus obtained 

 into the modes of transmission of force in solids. 



Let us consider a solid of any homogeneous elastic material, possessed 

 only of such symmetry of shape as will ensure that if it falls under 

 gravity in a liquid, each element will move vertically. Take the 

 origin of rectangular Cartesian co-ordinates at the centre of gravity, 

 the axes of x and y being horizontal, and the axis of z being drawn 

 vertically downwards. At time t let f be the depth of the C.G. below^ 

 a horizontal plane in the liquid, the pressure on which is uniform 

 and equal to II. The existence of gaseous pressure on the liquid 

 surface would only contribute to II wdthout modifying the general 

 conditions of the problem. 



Consider first the elementary hydrostatical theory, according to which 

 the liquid pressure at any point x, y, z on the surface of the solid acts 

 along the normal, and is equal to 



n + gp'(t+z), 



where p is the density of the liquid, supposed uniform. 



If the solid fall or rise very slowly, and the viscosity of the liquid 

 is very small, the results based on the hydrostatical theory ought to 

 give a close approximation to the truth. 



VOL. lxviii. s 



