The Bearing of Rotation on Relativity, 67 



which is a product in the collateral actinium series. But 

 the difficulties here are not inconsiderable aside from the 

 fact that the existence of such an isotope is somewhat diffi- 

 cult to imagine. If present in amounts proportional to the 

 actinium this product would have to emit comparatively long 

 range (7'2 cm.) a-particles and would therefore have a very 

 short life period. Such a conclusion does not seem at all 

 probable in the light of our present knowledge. 



It is not impossible that the values accepted for the ranges 

 of the a-particles from uranium are considerably in error and 

 that this is the reason for the lack of agreement between theory 

 and experiment. But until some more definite data have 

 been obtained there seems to be little justification for abstruse 

 speculation on the genetic relationship in the earlier stages 

 of the uranium series. 



Summary. 



The relation oE the activity of radium to the activity of 

 the uranium with which it is in radioactive equilibrium has 

 been redetermined. The results obtained indicate that if the 

 activity of uranium is taken as unity the activity of the 

 radium is equal to approximately 0*49. 



The total activity of uranium mixed with equilibrium 

 quantities of its disintegration products has been compared 

 with the activity of the uranium alone, and the former has 

 been found to be 4*73 times the latter. 



A critical examination has been made of the various 

 theories which have been proposed to explain the genesis of 

 radium and actinium from uranium. None of these theories 

 appears to satisfy the necessary requirements. 



V. The Bearing of Rotation on Relativity. 

 By Prof. R. A. SampsOx\, F.R.S.* 



CONSIDER two concentric spheres with a very small 

 space between them so that we need not distinguish 

 between their radii. An observer A is placed on the outer 

 surface of! the inner sphere and an observer B on the inner 

 surface of the outer. All phenomena are supposed to pass in 

 the space between the two spheres. 



Reoard this system and its changes first from a purely 

 geometrical point of view. A and B will possess in common 

 a natural unit of length, being the circumference of their 

 * Communicated by the Author. 

 F 2 



