82 Space and its Dimensions. [February, 
nature of solids. He exclaims, after summarising the gene- 
ration of a line from a point and of a square from a line : — 
“ In three-dimensions did not a moving square produce that 
blessed being a cube, with eight terminal points ? And in 
four dimensions shall not the motion of a divine cube result 
in a still more divine organisation with sixteen terminal 
points ? Behold the infallible confirmation of the series, 
2, 4, 8, 16 : is not this a geometrical progression ? Is not 
this, if I might quote my Lord’s own words, — ‘ stridtiy ac- 
cording to analogy ?’ 
I ask is it not the fadt that ere now your countrymen have 
witnessed the descent of beings of a higher order than their 
own, entering closed rooms, even as your Lordship entered 
mine without the opening of doors or windows, appearing 
and vanishing at will ?” 
As the reward of his pertinacity he is precipitated back 
into Flatland, where his after-fates need not concern us. 
Now all this, it may be said, affords no demonstration of 
polydimensional space and of the existence of beings able 
to see and adt in such space. But it supplies us at least 
with a chain of analogies which the great principle of con- 
tinuity bids us at least to deal with respedtfully. It 
further proves why and how we cannot diredtly pidture to 
ourselves space of higher dimensions than our own. 
The mere possibility of such space — of a fourth dimension 
— is a serious consideration. We shall find on reflection 
that much which on the hypothesis of three dimensions as 
the only conceivable seems absolutely impossible becomes 
easy, whilst the very foundations of the more exadt sciences 
will be found to be simply subjective, having their bases 
merely in the limitations of the percipient Ego. In this 
diredtion, be it remembered, all science is slowly but surely 
tending. 
It seems to us impossible that any being should enter into 
a closed room having no aperture in ceiling, walls, and 
roof ; should see and describe the contents of a locked box 
or drawer without unlocking or breaking it open, and should 
take out certain articles and introduce others. 
But the comparison with space of two dimensions will 
render such feats easy to a four-dimensional being. Let us 
suppose a Flatlander, a being with faculties something like 
our own, but possessing length and breadth only without 
thickness. We draw around him a continuous line in the 
form of square, triangle, circle, or other plane figure. It is 
obvious he cannot escape without rupturing the enclosure. 
Or, if we place him outside such a figure, he will be unable 
