Solutions of the bi-harmonic equation valid in the region bounded externally by parallel lines and internally by a circle midway between the lines have been given by one of the Authors in a recent paper . These solutions were adapted to the requirements of certain problems in the theory of elasticity, but modified solutions satisfying the boundary conditions characteristic of viscous fluid motion are easily derived. These modified solutions will here be given and will be used to find the stream function corresponding to the slow rotation of a cylinder placed symmetrically between parallel walls.
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