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XXXIX. Hie Problem of Uniform Rotation treated on the 

 Principle of Relativity. By H. Donaldson, B.A., 

 B.Sc, Scholar of Sidney Sussex College, Cambridge, and 

 Gr. Stead, B. A.., late Scholar of Clare College, Cambridge *. 



IX a previous paper (Phil. Mag. July 1910) we com- 

 menced an investigation of the above problem, dealing- 

 only with the changes in the dimensions of a rotating disk. 

 We showed that the contractions demanded by the relativity 

 theory, due to the motion of the disk, are fulfilled if the disk 

 buckle into a cuplike form, whose section by a vertical 

 plane is an epicycloid of intrinsic equation 



2 c . <f> 

 s = -~ - sin -. 



Fig. 1. 



In the figure shown we have 



y — s (l — v 2 /c 2 y 



■(-•-?)-' 



where v is the linear velocity of any point on the disk (=ya>). 

 We shall find that this cuplike form of the disk gives a 

 most useful method of visualising the processes going on 

 during the rotation on relativity hypotheses. For, if the 

 disk were considered as remaining plane, we should have, 

 owing to the lessening of the circumference and the in- 

 variability of the radius, a change in the value of the 

 " constant " tt, whereby we are transformed to a u real 



* Communicated by the Authors. 



