228 On Space of Four Dimensions . [April , 
treatise, which is of the highest interest, the author describes 
experiments which he made in Leipzig, in December, 1877, 
with Mr. Henry Slade, the American. These experi- 
ments were only the practical application of Gauss’s and 
Kant’s theory of space, which these two eminent men 
imagined might contain more than three dimensions. The 
author will try to give to the readers of the “ Quarterly 
Journal of Science ” an idea of this theory, though he must 
of course refer to the work itself for a more ample explana- 
tion of it. 
In accordance with Kant, Schopenhauer, and Helmholtz, 
the author regards the application of the law of causality as 
a function of the human intellect given to man a priori 
— i.e. f before all experience. The totality of all empirical 
experience is communicated to the intellect by the senses — 
i.e., by organs which communicate to the mind all the 
sensual impressions which are received at the surface of our 
bodies. These impressions are a reality to us, and their 
sphere is two-dimensional, acting not in our body, but only 
on its surface . 
We have only attained the conception of a world of 
objects with three dimensions by an intellectual process. 
What circumstances, we may ask, have compelled our intellect 
to come to this result ? If a child contemplates its hand, it 
is conscious of its existence in a double manner — in the first 
place by its tangibility, in the second by its image on the 
retina of the eye. By repeated groping about and touching, 
the child knows by experience that his hand retains the 
same form and extension through all the variations of dis- 
tance and positions under which it is observed ; notwith- 
standing that theform andextension of the image on the retina 
constantly change with the different position and distance of 
the hand in respeCt to the eye. The problem is thus set to 
the child’s understanding, Howto reconcile to its comprehen- 
sion the apparently contradictory faCts of the invariableness of 
the objeCt, together with the variableness of its appearance. 
This is only possible within space of three dimensions, in 
which, owing to perspective distortions and changes, these 
variations of projection can be reconciled with the constancy 
of the form of a body. 
So, likewise, in the stereoscope, the representation of the 
corporeality — i.e., of the third dimension — springs up in 
our mind when the task is presented to our intellect to refer 
at once two different plain pictures, without contradiction, to 
one single objeCt. 
Consequently our contemplation of a three-dimensioned 
