THE RECOGNITION OF THE FOURTH DIMENSION. 193 
fluid—that is, one without friction of one moving portion 
or another. In such a medium vortices would be indestruct¬ 
ible. They would go on forever, altering their shape, but 
consisting always of the same portion of the fluid. But a 
straight vortex could not exist surrounded entirely by the 
fluid. The ends of a vortex must reach to some boundary 
inside or outside the fluid. 
A vortex which is bent round so that its opposite ends 
join is capable of existing, but no vortex has a free end in 
the fluid. The fluid round a vortex is always in motion, 
and one produces a definite movement in another. 
Lord Kelvin has proposed the hypothesis that portions of 
a fluid segregated in vortices account for the origin of matter. 
The properties of the ether in respect of its capacity of prop¬ 
agating disturbances can be explained by the assumption 
of vortices in it instead of by a property of rigidity. It is 
difficult to conceive, however, of any arrangement of the 
vortex rings and endless vortex filaments in the ether. 
Now, the further consideration of four-dimensional rota¬ 
tions shows the existence of a kind of vortex which would 
make an ether filled with a homogeneous vortex motion 
easily thinkable. 
To understand the nature of this vortex, we must go on 
and take a step by which we accept the full significance of 
the four-dimensional hypothesis. Granted four-dimensional 
axes, we have seen that a rotation of one into another leaves 
two unaltered, and these two form the axial plane about 
which the rotation takes place. But what about these two ? 
Do they necessarily remain motionless? There is nothing 
to prevent a rotation of these two, one into the other, taking- 
place concurrently with the first rotation. This possibility 
of a double rotation deserves the most careful attention, for 
it is the kind of movement which is distinctively typical of 
four dimensions. 
Rotation round a plane is analogous to rotation round an 
axis. But in three-dimensional space there is no motion 
analogous to the double rotation, in which, while axis 1 
changes into axis 2, axis 3 changes into axis 4. 
