Transverse Oscillations of a Canal of Circular Section. 325 



earth the action of the thorium family as well as that of 

 the uranium family should be taken into consideration. 



Strutt found that the average amount of radium present 

 in the surface rocks was 5 x 10 ~ 12 gram per c.c. Taking 

 the life of thorium as 10 9 years and that of radium as 2 X 10 3 

 years, we see from our previous values that there must be 

 about 7 x 10 5 as much thorium as radium, i. e. there must 

 be about 10~ 6 gram per c.c. This amount is of course still 

 very small, only amounting to about 10 -5 per cent, of the 

 whole mass. 



S. J. Allen, working in Pittsburg, Conn., has lately 

 published a paper on " Radioactivity in a Smoke-laden 

 Atmosphere " *. He finds the same type of results for 

 negatively charged wires and obtains no activity on positively 

 charged ones. With wires, however, suspended in the 

 atmosphere without charge, he obtains about 25 per cent, of 

 the activity found on a negatively charged one. 



Similar experiments were made in the present case during 

 smoky fogs, and although the wires when drawn in were 

 always covered by a thick layer of dirt, no activity was 

 observed either on a positively charged wire, or on one 

 which had been suspended in the atmosphere for six weeks 

 without charge. 



I wish to thank Prof. Rutherford for suggesting the 



no o 



experiments and for his valuable help and encouragement 

 from time to time. 



Physical Laboratory, 



The University, Manchester. 



Sept. 1908. 







XXVIL The Transverse Oscillations of a Canal of Circular 

 Section. By Robert A. Houstoun, ALA., Ph.D., D.Sc. f 



fT^HE problem of the transverse oscillations of water con- 

 X tained in a canal of circular section has not yet been 

 solved, though Lord Rayleigh has made an approximate 

 determination of the frequency of the slowest mode by a 

 general method for the case, where the surface is at the 

 level of the axis J. The object of this note is to show how 

 the same case may be solved by the substitution of a series. 



Take the origin at the centre of the circle. Let the axis 

 of x be horizontal and the axis of y be measured positively 



* Pkys. Rev. Dec. 1907. 



t Communicated by Prof. A. Gray, F.R.S. 



% Lamb's Hydrodynamics, 3rd edition, § 256. 



Phil Mag. S. 6. Vol. 17, No. 98. Feb. 1909. Z 



