Taking Ox along OS, the Stokes' function at P for the source S is p cos **PSx**, and of the source H and line sink OH is p(a/f) cos PHx and - (p/a) (PO - PH); so that = p (cos **PSx**+f cos PHx PO a PH), (q) and Ili = -p, a constant, over the surface of the sphere, so that there is no flow across.

For a doublet at S, of moment m, the Stokes' function is M f cos **PSx** = - m p s3; and for its image at H the Stokes' function is m f cos PHx =m f 3 PH" (6) so that for the comnation _ a3 I I 2 4)-myb12 (f 3 PH PS 3) =m f 3 (pa ll 3 P53)' 3 and this vanishes over the surface of the sphere.

Hence, forming the equation of motion of a masselement, plx, we have **pSx**.fi=I(P.Oy/8x).