of Edinburgh, Session 1875 - 76 . 
67 
vanic circuit, or galvanic circuits, of the same shape as the core or 
cores. The setting forth of this analogy to people familiar, as 
modern naturalists are, with the distribution of magnetic force in 
the neighbourhood of an electric circuit, does much to promote a 
clear understanding of the still somewhat strange fluid motions 
with which we are at present occupied. 
15. To understand the motion of the liquid in the rotational 
core itself, take a piece of Xndian-rubber gas-=pipe stiffened internally 
with wire in the usual manner, and with it construct any of the 
forms with which we have been occupied, for instance the sym- 
metrical trefoil knot (fig. 8, § 13), unit- 
ing the two ends of the tube carefully 
by tying them firmly by an inch or two 
of straight cylindrical plug, then turii 
the tube round and round, round its 
sinuous axis. The rotational motion of 
the fluid vortex core is thus represented. 
But it must be remembered, that the 
outer form of the core has a motion per- 
pendicular to the plane of the diagram, 
and a rotation round an axis through the centre of the diagram, 
and perpendicular to the plane in each of the cases represented by 
the preceding diagrams. The whole motion of the fluid, rotational 
and irrotational, is so related in its different parts to one another, 
and to the translational and rotational motion of the shape of the 
core, as to be everywhere slipless. 
16 . Look to the preceding diagrams, and, thinking of what they 
represent, it is easy to see that there must be a determinate parti- 
cular shape for each of them which will give steady motion, and I 
think we may confidently judge that the motion is stable in each, 
provided only the core is sufficiently thin. It is more easy to 
judge of the cases in which there are multiple sinuosities by a 
synthetic view of them (§ 3) than by consideration of the maxi- 
mum-minimum problem of § 8. 
17. It seems probable that the two- or three- or multiple- 
threaded toroidal helix motions cannot be stable, or even steady, 
unless I, fx, and N are such as to make the shortest distances 
between different positions of the core or cores considerable in 
VOL. IX. 
K 
