THE RECOGNITION OF THE FOURTH DIMENSION. 199 
rounded by thirty others. Of these it touches ten, and, if it 
rotates, it drives the rest by the means of these. Now, if 
we imagine the central sphere to be given an A or a B rota¬ 
tion, it will turn the whole mass of spheres round in a 
systematic manner. Suppose four-dimensional space to be 
filled with such spheres, each rotating with a double rota¬ 
tion, the whole mass would form one consistent system of 
motion, in which each one drove every other one, with no 
friction or lagging behind. 
Every sphere would have the same kind of rotation. In 
three-dimensional space, if one body drives another round, 
the second body rotates with the opposite kind of rotation; 
but in four-dimensional space these fourr-dimensional spheres 
would each have the double negative of the rotation of the 
one next it, and we have seen that the double negative of 
an A or B rotation is still an A or B rotation. Thus four¬ 
dimensional space could be filled with a system of self-pre¬ 
servative living energy. If we imagine the four-dimensional 
spheres to be of liquid and not of solid matter, then, even if 
the liquid were not quite perfect and there were a slight 
retarding effect of one vortex on another, the system would 
still maintain itself. 
In this hypothesis we must look on the ether as possessing 
energy, and its transmission of vibrations, not as the con¬ 
veying of a motion imparted from without, but as a modifi¬ 
cation of its own motion. 
We are now in possession of some of the conceptions of 
four-dimensional mechanics, and will turn aside from the 
line of their development to inquire if there is any evidence 
of their applicability to the processes of nature. 
Is there any mode of motion in the region of the minute 
which, giving three-dimensional movements for its effect, 
still in itself escapes the grasp of our mechanical theories? 
I would point to electricity. Through the labors of Fara¬ 
day and Maxwell we are convinced that the phenomena of 
electricity are of the nature of the stress and strain of a 
medium; but there is still a gap to be bridged over in their 
