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III. On the Hotation of Slightly Elastic Bodies. By 

 Dorothy Wrinch, D.Sc, Fellow of Girton College, 

 Cambridge, and Member of Research Staff, University 

 College, London * . 



THE change in dimensions of a slightly elastic body due 

 to rotation is a question of some practical importance, 

 and does not appear to have received any systematic treat- 

 ment. In the theory of elasticity, the displacements of a 

 point of the body are of course discussed and the displace- 

 ments of the points of the boundary determine the increase 

 of dimensions. But the problems of elasticity which are of 

 interest mainly from the point of view of increase of dimen- 

 sions, rather than of the distribution of stress in the material, 

 can rarely be solved by the current methods or appear onlv 

 as special cases of a general mode of analysis. Even the 

 simple problem of a circular cylinder of finite length, rotating 

 about its axis, has not yet admitted an exact solution, though 

 an approximate solution, which becomes valid when the 

 cylinder is of infinite length, has been given by Chree. 

 When the cylinder has a finite length, the surface con- 

 dition of zero traction over the curved surface is violated, 

 and instead of this traction becoming zero at all points on 

 the surface, only its average value over the surface is zero. 

 The results for the case of an infinite cylindrical annulas 

 do no.t appear to be on record, and they are interesting on 

 account of their marked divergence from those which belong- 

 to the complete disk. 



In the present paper we group together some of the 

 simpler and more interesting solutions of problems of 

 this type, including those of the infinite circular cylinder 

 and the infinite cylindrical annulus. These specific pro- 

 blems are solved to any degree of approximation and for a 

 non- uniform distribution of density. The analysis is simpler 

 than is usual, for it does not seem necessary to treat these 

 comparatively simple problems as special cases of general 

 theory, and it is desirable, at least in the interests of the 

 engineer or physicist, that a fundamentally simpler treat- 

 ment should be placed on record. It also seems possible 

 that such solutions may be of interest with regard to 

 scientific instruments of great precision, in which some 

 portion of the apparatus is in rotation, or, on the larger 

 scale, in problems of practical engineering. Although no 



* Communicated by the Author. 



