On Water-Waves as Asymmetric Oscillations. 713 



Note. — A. G-ockel (Jalirbuch der Radioahtivitat, vii. p. 503, 

 1910), examined various minerals found by Prof. Strutt to 

 be relatively rich in radium, and obtained radium contents 

 far below his values, accompanied at the same time by 

 unusually high thorium richness. Grockel suggests the possi- 

 bility of a source of error from the active deposit of thorium, 

 consequent upon the introduction of thorium emanation into 

 the electroscope. 



Some experiments were made to test the possibility of 

 such an error affecting the estimation of radium in bodies 

 rich in thorium. 



A solution containing as much as O'l gram thorianite, 

 having been first boiled to expel radium emanation, was then 

 treated in the same manner as that employed in the esti- 

 mation of radium. Four experiments were made using both 

 slow and fast admission, in the latter case the gases being- 

 admitted into the electroscope as fast as the safety of the 

 gold leaf would permit. The whole of the gases were in 

 this case transferred to the electroscope within two minutes 

 subsequent to being cut off from the parent solution. In no 

 case was any certain increase noticed in the rate of collapse of 

 the leaves of the electroscope in three hours after admission. 



In view of the fact that no effect v T as observable in the 

 case of a solution so rich in thorium, it is safe to infer that 

 in no case could the leak of an electroscope be noticeably 

 affected as read three hours after the slow admission of such 

 quantities of thorium emanation as are associated with 

 amounts of thorium of the order of magnitude dealt with in 

 the estimation of rocks and minerals. 



= — -. 



X'CII. On Water Waves as Asymmetric Oscillations and on the 

 Stability of Free Wave- I rains. By Andrew Stephenson*. 

 1. T1TATER waves furnish a complex example of asvm- 

 ' » metric oscillations, and it is natural to inquire 

 whether they exhibit the marked energy absorption under 

 direct force of double frequency, which is characteristic of the 

 asymmetric system with one degree of freedom."!"- The problem 

 is most simply considered as one of steady motion. Direct 

 force may be applied to a deep stream flowing uniformly by 

 a stationary periodic variation of pressure along its surface. 

 Such variation will produce standing waves of equal length. 

 Is this state of motion stable when the wave-length is halt' 

 that of the free standing waves ? 



For the purpose of testing the stability of a. train of waves 



* Communicated by the Author. 



t "On a Peculiar Property of the Asymmetric System." Phil. Mug- 

 Jan. 1911. 



