VI. On a spherical vortex

Abstract

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 r 2 ( r 2 / a 2 + ( z -Z) 2 / c 2 - 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