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XXX. 
ox THE STABILITY AXD SMALL OSCILLATION OF A 
PERFECT LIQUID FULL OF XEAELY STRAIGHT CORE- 
LESS VORTICES. By SIR W. THOMSOX, F.R.S., Hon. 
Mem. R.I.A. (Plate XIX.) 
(EXTEACT FROM A LeTTER TO PeOFESSOE FiTZ GeRALD.) 
[Read November 30, 1889.] 
I have quite confirmed one thing I was going to write to you 
(in continuation with my letter of October 26) viz. that rotational 
vortex cores must be absolutely discarded, and we must have nothing 
but irrotational revolution and vacuous cores. So not to speak 
of my little piece of coreless vortex work (' Yibrations of a Columnar 
Yortex,' Proc, R.S.E., March 1, 1880), Hick's Paper, * On the 
Steady Motion and small Yibrations of a Hollow Yortex ' Transac- 
tions, Roy. Society, 1884), will be the beginning of the Yortex 
Theory of ether and matter, if it is ever to be a theory. Steady mo- 
tion, with crossing lines of vortex column, is impossible with rota- 
tional cores, but is possible with vacuous cores and purely irrotational 
circulations around them. The accompanying diagram (Fig. 1, PL xix.) 
helps to explain by an illustration. It shows the shape of an in- 
finitely long cylindrical vacuous vortex column as disturbed by a rigid 
tore,^ held fixed in a plane perpendicular to the axis of the column, and 
having irrotational circulation through itself. Blue represents vacuum ; 
the white on each side, liquid ; and the two black circles section of 
the tore. The curves representing the boundary of the vortex are 
calculated to give uniform resultant fluid velocity over the whole 
surface of the hollow core. This velocity is the resultant of the 
velocities due to the circulation around the vacuous core, and to circu- 
lation through the tore. The former is rigorously in inverse propor- 
tion to distance from the axis of the vacuous column. The latter 
is approximately parallel to this axis, and in inverse proportion to 
^ Or circular ring of circular cross section, like an anchor ring. 
