592 



Mr. D. Coster on the Rotational Oscillation, 



The condition c\i ^10 means that the radius of the 

 cylinder must be about equal to or larger than the wave- 

 length. If R is small compared with X the second part of 



1 

 09 





0-8 





0-7 





0-6 





0-5 

 0-4 

 0-3 



■J mod. 





0-2 





0-1 



iiii 



10 



the friction al couple is negligible. For |cR|^10 the second 

 term on the right-hand side of (10) becomes : 



acie = — ake 



I since c = ke J. 

 Hence equation (11) now becomes : 



K= — \irfj\Vw — 'Itt/jl/cR- 1 .-(aco<(pt-f- jj J 



(13) 



where 



d 



&)= -rifacospt). 



The frictional couple thus divides into two parts, one of 

 which does not contain the density of the liquid, and another 

 in which it occurs and which therefore refers to the emission 

 of waves. In the transition to the limit of uniform rotation 

 the first part only remains. 



In the discu-sion of the second part of the frictional 



moment the quantity k = x/~ is an important factor. If 

 we take a time of oscillation of 2tt seconds, so that^=-l, wo 



have k 



This gives the following values for k : 



V> =1) - 



Water 16° 



. 1 



. 0-0013 



'. 0-0000898 



0011 

 0-000171 



0000085 



9o 



Atm. air 0° 



Air 001 atm* 



2-8 

 0-28 



Air 0001 atm.* 



Hydrogen 1 atm. 0° .. 



009 

 1 



' * At these pressures /u has not become much smaller. Cf. Kundt u. 

 Warburg, Pogg. Ann. 1875, Band civ. 



