Fvnsv.n — Ajj/j/icaf/'omi of BrsscTs FnuctionK to Tlnixics. fi.'i 



If r bo small compared with {a), wo shall have 

 (or = Qr (1 - 



where 



1 ^ 



€ = —= n = - 



|D7r , P 

 4rt 



J 



II. Vortex Decay. 



The vessel having arrived at a unifonn state of spin, the containing 

 cylinder is stopped. 



We have in this case 



^ now vanishing for ^ oo , this gives 



(ur- = 22 — e-'"trJ, (a,„r) + F{t). 



The conditions are now (1) for r = a at all times w = 0. This 

 gives, as before, J, (a„,rt) = 0, F{t) = 0. (2) For / = 0, w = fi. 

 This gives 



fir + 22 -^/i(a„/), 



whence we have 



fi 



(ma) ' 



giving now 



u>r = - 2fi2^ P 



as before, when t is large, we may reduce the 2 to its first term. 



Decay of Energy. 



The kinetic energy 



TT - pTT I {ioryrdr 



= 4fiV2« P 



1 f 



— r/f {a J I 



a.,- 



