nted by 3^2; it must be that a
Square of three inches every way, moving somehow parallel to itself
(but I don't see how) must make Something else (but I don't see what)
of three inches every way--and this must be represented by 3^3."

"Go to bed," said I, a little ruffled by this interruption: "if you
would talk less nonsense, you would remember more sense."

So my Grandson had disappeared in disgrace; and there I sat by my
Wife's side, endeavouring to form a retrospect of the year 1999 and of
the possibilities of the year 2000, but not quite able to shake off the
thoughts suggested by the prattle of my bright little Hexagon. Only a
few sands now remained in the half-hour glass. Rousing myself from my
reverie I turned the glass Northward for the last time in the old
Millennium; and in the act, I exclaimed aloud, "The boy is a fool."

Straightway I became conscious of a Presence in the room, and a
chilling breath thrilled through my very being. "He is no such thing,"
cried my Wife, "and you are breaking the Commandments in thus
dishonouring your own Grandson." But I took no notice of her. Looking
round in every direction I could see nothing; yet still I FELT a
Presence, and shivered as the cold whisper came again. I started up.
"What is the matter?" said my Wife, "there is no draught; what are you
looking for? There is nothing." There was nothing; and I resumed my
seat, again exclaiming, "The boy is a fool, I say; 3^3 can have no
meaning in Geometry." At once there came a distinctly audible reply,
"The boy is not a fool; and 3^3 has an obvious Geometrical meaning."

My Wife as well as myself heard the words, although she did not
understand their meaning, and both of us sprang forward in the
direction of the sound. What was our horror when we saw before us a
Figure! At the first glance it appeared to be a Woman, seen sideways;
but a moment's observation shewed me that the extremities passed into
dimness too rapidly to represent one of the Female Sex; and I should
have thought it a Circle, only that it seemed to change its size in a
manner impossible for a Circle or for any regular Figure of which I had
had experience.

But my Wife had not my experience, nor the coolness necessary to note
these characteristics. With the usual hastiness and unreasoning
jealousy of her Sex, she flew at once to the conclusion that a Woman
had entered the house through some small aperture. "How comes this
person here?" she exc