The Republican. [volume] (Oakland, Md.) 1877-current, 1884-12-20

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a stone dropped from his hand any
where onto the plane must fall toward
the center of the cube; its fall must be
slanting when the man stands any
where but at the planes middle point,
and the further away he is the more the
stone must slant. 1t would not drop at
right angles TO the surface, as it would
on the earth. but at an angle varying
according TO circumstances, and, Just as
the stone slants in falling, the man S
body would slant in standing. BY great
exertion he might do what we call stand
ing, but generally when he occupied that
position he would accidentally have
stumbled into it. His houses would all
| have to slant in the same way; trees
would grow SO, and rain would fall So"
"What an extremely absurd situation
for human being to occupy" exclaimed
the writer.
eve have something analogous to it
on the earth" continued Dr. Vankirk.
I'VE are in precisely such a position
when we climb hill, and houses built
on hillside stand at some other than a
right angle to its sloping side. Between
ourselves and our friends on the cubical
| planet there is, however, this important
difference. We actually ascend hills
when we slant, but, by hypothesis, our
friend walks along surface all plane
when he slants, and the nearer he gets
to its edge the more he
slants The effect upon him can,
however, be none other than
that he is going up an activity, and
this must be his impression. For, con-
slider the matter for moment. A
mountain peak is higher than the COM
mon surface of the earth only because
its sumplit is further away from the
earth's center than is the plain at its
base Our traveller on the cubical
planet gets at every step further from
/ the center of the cube, and consequently
at every step he ascends an ACTIVITY
and slants his body slightly to keep in
line with gravity. The further he gets
from the starting point we have given
him the more he slants-that is to say,
the sleeper becomes his hill, until at
last, when he comes to the edge of the
plane; he seems to stand upright once
more, and on the summit of mountain,
and instead of lying on his face to look
down the jumping-off place he looks
down into two valleys from his noun
tain top, the one valley being the plane
along which he has been iourneving
and the other being the adjacent side
of the cube. If, instead of going to the
edge of the plane he has travelled to one
of the four corners he has only assembled.
and, with ever increasing difficulty, one
OF four enormous, overlapping noun
tains as much higher in proportion than
the ridge along the edge, as the hv-
pothenuse of right angled triangle is
longer than either of its sides Do YOU
get my meaning?"
has been going up hill all the way, for
ne has been getting further from the
center of the cube"
"And if he had gone to the opposite
edge of the square he would have gone
up another hill, and so on, all around
the square, which would be an oblong
hollow, or cusp, or cup" continued the
doctor, "having as its lowest point the
middle point of the square. There can
be no escape from this conclusion. You
or l, If we were now placed on such a
planet, would know that in walking to
one of its edges we had gone up hill,
and this view of the matter would be
confirmed when, placing a round stone
on our mountain side, we had seen it
roll down into the valley. What would
be true, however, is that it would have
rolled merely from the edge of plane
square surface to its middle point in or
der to get as near as possible to the
center of the cube, which is the radiating
point of gravitation."
Exactly" said the writer. Nov"
DR.. Vanllirk went on, warming up to his
subject, the surface along which our
friend has been journeying is, by hy-
pothesis, plane--a square-and line
drawn diagOnally from one corner to an
other will lie wholly on the surface. will
be straight line, and will be the short
est distance between those two points.
But the man who has climbed to the
summit of one of those towering noun
tains will know with certainty that
nothing can shake, that that line which
joins the two corners is a curve begin
ming at his feet, running into the vale
and then ascending to the summit of the
opposite mountain. What to him will
be the straight line and shortest dis
lance from the one cliff to the other will
then really be a curve arched over the
square from corner to corner. But
he himself, though gifted with the
mind of a Newton or Pascal,
could never discover this, for it is
only by hypothesis that we ourselves
know otherwise. The system of which
he was part would compel him to hold
the straight line to be the curve and the
curve the straight line. Gravitation
would have done the business for his
mind. Light, which seems to us to
come in straight lines, to him would
come in curves, so that, as said at first,
he would always see around a corner,
just as we can when light is refracted
or reflected. But the main point is that
his straight line being entirely different
from ours, his mathematics, astronomy,
molecular physics and physical science
in general would be different. They
would be logical, no doubt, and since
science would explain phenomena and
easily lead to the foretelling of events
like eclipses and so on, it would be true
quite rs true as our own absolutely
true mathematics.
But it seems to me, DOCTOR" said
the writer. ''that though our traveller on
the cubical planet would feel in his body
and leUS that he had cone IN hill VET