VI. On a spherical vortex

In a paper published by the author in the ‘Philosophical Transactions’ for 1884, “On the Motion of Fluid, part of which is moving rotationally and part irrotationally,” a certain case of motion, sj^mmetrical with regard to an axis, was noticed (see pp. 403-405). Taking the axis of symmetry as axis of z, and the distance of any point from it as r, and allowing for a difference of notation, it was shown that the surfaces r2 (r2 / a2 + (z-Z)2 / c2 - 1) = constant, where a, c are fixed constants, and Z any arbitrary function of the time, always contain the same particles of fluid in a possible case of motion