Elastic Solids at Best or in Motion in a Liquid. 



245 



g (p - p), on the other hand, depend largely on the shape of the 

 ellipsoid. 



Thus, denoting them by a, /3', y, we have approximately, in the 

 case of a very elongated ellipsoid, whose long axis is vertical, 



} 



.(29); 



and, except in the immediate vicinity of the central section z = 0, we 

 may take in place of (29) 



,(30). 



In a very flat ellipsoid, approximating to a disc, with the short axis 

 vertical, we have approximately 



«' = g{p-p')xz{^-^)i{^c% 

 P = g{p-ply^-^)i{^% 



y = -g(p- p) [(« 2 - rt 2 ) & + (& 2 - w 2 ) f + v (tf + & 2 )* 2 ] - (6Ec 2 ) 



. (31). 



Except close to the vertical diameter, the terms in z 2 in y would be 

 relatively negligible, while, in general, a! and /3' would be small com- 

 pared to y . 



In the case of the sphere it is perhaps more convenient to record the 

 complete solution, viz., 



%lx 



xx = yy = - II - gp'ut + ±g(p - ip')t 

 zz = -II-gput-lg(p + 2p)z, 

 xy = 0, 



xz/x = yz/y = -\g(p- p ') 



(32); 



r - -^[(n+^)^+^ 2 -^ 2 -^)] 



.(33). 



[IfarcA 13, 1901.] — The paper as originally presented to the Society 

 dealt briefly with two or three other details. It showed how the solu- 

 tion in § 6 depended not on the viscous resistance varying as the first 

 power of the velocity in the final state, but on its varying over the 



