Purser — Applications of Besscl^s Functions to P/it/sics. 47 

 in problem (E). Then from bottom of cylinder to disk, we have 



= a2 + XnPJ {mz) J,{mr) + X,B,,K,{nr) sin {nz\ 

 the m system being determined by /i {mR) = 0, the 71 system by 



Sir 



'' = T 



below the disk, and above 



az I - C 

 to which will correspond 



^ = ^ f ^' - I '^') + 2^ — J,{mr) - 2„ - BnKi'ir) cos nz, 



below the disk, and above 



^ 1 — 

 ~ ^ B^^K^nr cos W2 + C. 



The constant C will be determined by the consideration that, at 

 the disk 2 = ^, the lower and upper <^ coincide, for r = R. 

 This gives 



a 



Referring to the value of yS„, in potential problems, it is easily 

 seen that the last term on the left-hand side is, in general, 

 negligible, so that we may write 



Now, the kinetic energy T of the fluid 



when is the discontinuity of This discontinuity now 



= a y!— i _ ;.2^ ^ discontinuity of terms in JJ^mr). 



