science has ever applied. The usual argument by which we
prove to our children the earth's rotundity is not purely geometric.
When, standing on the seashore, we see the sails of a ship on
the sea horizon, her hull being hidden because it is below, the
inference that this is due to the convexity of the surface is based
on the idea that light moves in a straight line. If a ray of light
is curved toward the surface, we should have the same appearance,
although the earth might be perfectly flat. So the Koresh people
professed to have determined the figure of the earth's surface by
the purely geometric method of taking long, broad planks, perfectly
squared at the two ends, and using them as a geodicist uses his base
apparatus. They were mounted on wooden supports and placed end to
end, so as to join perfectly. Then, geometrically, the two would
be in a straight line. Then the first plank was picked up, carried
forward, and its end so placed against that of the second as to fit
perfectly; thus the continuation of a straight line was assured.
So the operation was repeated by continually alternating the planks.
Recognizing the fact that the ends might not be perfectly square,
the planks were turned upside down in alternate settings, so that
any defect of this sort would be neutralized. The result was that,
after they had measured along a mile or two, the plank was found to
be gradually approaching the sea sand until it touched the ground.

This quasi-geometric proof was to the mind of Koresh positive.
A horizontal straight line continued does not leave the earth's
surface, but gradually approaches it. It does not seem that the
measurers were psychologists enough to guard against the effect of
preconceived notions in the process of applying their method.

It is rather odd that pure geometry has its full share of paradoxers.
Runkle's "Mathematical Monthly" received a very fine octavo volume,
the printing of which must have been expensive, by Mr. James Smith,
a respectable merchant of Liverpool. This gentleman maintained that
the circumference of a circle was exactly 3 1/5 times its diameter.
He had pestered the British Association with his theory, and come
into collision with an eminent mathematician whose name he did
not give, but who was very likely Professor DeMorgan. The latter
undertook the desperate task of explaining to Mr. Smith his error,
but the other evaded him at every point, much as a supple lad might
av