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VI. On a Spherical Vortex. 
By M. J. M. Hill, M.A., D.Sc., Professor of Mathematics at University College, 
London. 
Communicated hy Professor Heneici, F.R.S. 
Received January 19,—Read March 1, 1894. 
1. 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, symmetrical 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 
P ~ ~ 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. 
The surfaces are of invariable form. If the constant be less than — the 
surfaces are imaginary; if the constant lie between — ^a^ and zero they are ring- 
shaped ; if the constant be zero, the single surface represented breaks up into an 
evanescent cylinder and an ellipsoid of revolution; if the constant be positive, the 
surfaces have the axis of revolution for an asymptote. 
The velocity perpendicular to the axis of symmetry is 
(z-Z); 
the velocity parallel to the axis of symmetry is 
• 91' I- 
where ^ is a fixed constant and Z = dZjdt. 
•2'). 7.91 
