104 Sir William Thomson on Vortex Statics. 



Fig. 6. Fig. 7. Fig. 8. " Trefoil Knot. 



14. The irrotational motion of the liquid round the rotational 

 cores in all these cases is such that the fluid-velocity at any 

 point is equal to, and in the same direction as, the resultant 

 magnetic force at the corresponding point in the neighbourhood 

 of a closed galvanic 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 distri- 

 bution 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 pre- 

 sent occupied. 



15. To understand the motion of the liquid in the rotational 

 core itself, take a piece of Indian-rubber gas-pipe stiffened in- 

 ternally with wire in the usual manner, and with it construct 

 any of the forms with which we have been occupied, for in- 

 stance the symmetrical trefoil knot Fi ,. 9 . "Nine-leaved Knot." 

 (ng. 8, % 13), uniting the two ends of 

 the tube carefully, by tying them 

 firmly, by an inch or two of straight 

 cylindrical plug ; then turn 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 

 perpendicular to the plane of the dia- 

 gram, 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 differ- 

 ent 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 determi- 



