The boundary conditions implied by conditions (t) and (it) are: For Eq. (4): (a) ue = 0, ur finite, when 0 = 0. (b) ur = ue = 0, when 6 = a. For Eq. (5): (c) us = 0, ur finite, dur/dd finite, when 6 = 0.* These yield respectively the equations: Cj cos2 a + c2 cos a + c3 = 0, 2ci + c2 = 0. These have ct = c2 = c3 = 0 as their only solution. As Squire [5] has shown, the general solution of Eq. (4) with = c2 = c3 = 0 is: where a is an arbitrary constant. Referring again to the boundary condition

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... (a) = ue(a) = 0, we see that there is no finite value of a{a = yields a satisfactory but trivial solution) which satisfies this boundary condition, no matter what value of a is chosen. Thus we have shown that there is no non-trivial solution of the form \p = rf(8) that is compatible with the Navier-Stokes equations and the boundary conditions (i) and (it). The author wishes to thank Prof. Garrett Birkhoff for suggesting the problem and for his helpful advice. *It is assumed that when these boundary conditions are substituted in Eqs. (4) and (5) that the limit d -> 0 is taken, since 6 = 0 is a singular point in the spherical polar coordinate system.