120 Prof* H. Lamb on the Uniform 



It is of some interest to apply the same method to the 

 two-dimensional problem of the flow past a circular cylinder 

 where, as is well-known, Stokes was led to the conclusion 

 that a steady motion is impossible. It will appear that when 

 the inertia terms are partially taken into account, in the 

 manner above explained, this conclusion is modified, and 

 that a definite value for the resistance is obtained. 



The hydrodynamical equations are now satisfied by 





(44) 



J> = />U|*, ...... (45) 



and 

 where 



r 73 .e 

 P rovided vr*=o, (46) 



(V 1 2 -2^) X = 0, (47) 



Vi 2 =c>7c^ 2 + BW (48) 



The appropriate solution of (47) is 



X = C^K (Ar), ...... (49) 



where * 



K„(fr)= -(,+ lo g lfc)l, (fo .) + «* + ** ( 1 + 1) + ... 

 V(i)--*{>-£ + T^.--}« 



Por small values of kr we have 



Xr~ PC 1 + **)(? + logi*r), . . . (51) 



wnence 



13* C r 3 i B 2 , -i 



(52) 



* The notation is that of Gray and Mathews, Treatise on Bessel 

 Functions, p. 68. 



