198 
HINTON. 
If we suppose the ether to have its properties of transmit¬ 
ting vibration given it by such vortices, we must inquire how 
they lie together in four-dimensional space. Placing a cir¬ 
cular disk on a plane and surrounding it by six others, we 
find that if the central one is given a motion of rotation, it 
imparts to the others a rotation which is antagonistic 
in every two adjacent ones. 
If A goes round as shown by 
the arrow, B and C will be 
moving in opposite ways, and 
each tends to destroy the mo¬ 
tion of the other. 
Now, if we suppose spheres to 
be arranged in a corresponding 
manner in three-dimensional 
space, they will be grouped in 
figures which are for three-di¬ 
mensional space what hexagons 
Fig. 15. 
are for plane space. If a number of spheres of soft clay be 
pressed together, so as to fill up the interstices, each will as¬ 
sume the form of a 14-sided figure, called a tetrakaidecagon. 
Now, assuming space to be filled with such tetrakaideca- 
gons and placing a sphere in each, it will be found that one 
sphere is touched by six others. The remaining eight 
spheres of the fourteen which surround the central one will 
not touch it, but will touch three of those in contact with it. 
Hence if the central sphere rotates it will not necessarily 
drive those around it so that their motions will be antago¬ 
nistic to each other, but the velocities will not arrange them¬ 
selves in a systematic manner. 
In four-dimensional space the figure which forms the next 
term of the series hexagon, tetrakaidecagon, is a thirty-sided 
figure. It has for its faces ten solid tetrakaidecagons and 
twenty hexagonal prisms. Such figures will exactly fill 
four-dimensional space, five of them meeting at every point. 
If, now, in each of these figures we suppose a solid four¬ 
dimensional sphere to be placed, any one sphere is sur- 
