THE RECOGNITION OF THE FOURTH DIMENSION. 181 
our conceptions are founded on the supposition of a space 
which is represented analytically by three independent axes 
and variations along them—that is, it is a space in which there 
are three independent movements. Any motion possible in 
it can be compounded out of these three movements, which 
we may call: up, right, away. 
To examine the actions of the very small portions of 
matter with the view of ascertaining if there is any evidence 
in the phenomena for the supposition of a fourth dimension 
of space, we must commence by clearly defining what the 
laws of mechanics would be on the supposition of a fourth 
dimension. It is no use asking if the phenomena of the 
smallest particles of matter are like—we do not know what. 
We must have a definite conception of what the laws of mo¬ 
tion would be on the supposition of the fourth dimension, 
and then inquire if the phenomena of the activity of the 
smaller particles of matter resemble the conceptions which 
we have elaborated. 
Nqw, the task of forming these conceptions is by no means 
one to be lightly dismissed. Movement in space has many 
features which differ entirely from movement on a plane • 
and when we set about to form the conception of motion in 
four dimensions, we find that there is at least as great a 
step as from the plane to three-dimensional space. 
I do not say that the step is difficult, but I want to point 
out that it must be taken. When we have formed the con¬ 
ception of four-dimensional motion, we can ask a rational 
question of Nature. Before we have elaborated our concep¬ 
tions we are asking if an unknown is like an unknown—a 
futile inquiry. 
As a matter of fact, four-dimensional movements are in 
every way simple and more easy to calculate than three-di¬ 
mensional movements, for four-dimensional movements are 
simply two sets of plane movements put together. It ap¬ 
pears to me one of the most marvelous characteristics of the 
power of the intellect to find how, without any of the fa¬ 
miliarity derived from experience, it is possible to grasp 
