in physics. Some of Euclid's axioms were felt to be not "necessary
truths," but mere empirical laws; in order to establish this view,
self-consistent geometries were constructed upon assumptions other
than those of Euclid. In these geometries the sum of the angles of
a triangle is not two right angles, and the departure from two right
angles increases as the size of the triangle increases. It is often
said that in non-Euclidean geometry space has a curvature, but this
way of stating the matter is misleading, since it seems to imply a
fourth dimension, which is not implied by these systems.

Einstein supposes that space is Euclidean where it is sufficiently
remote from matter, but that the presence of matter causes it
to become slightly non-Euclidean--the more matter there is in the
neighborhood, the more space will depart from Euclid. By the help of
this hypothesis, together with his previous theory of relativity, he
deduces gravitation--very approximately, but not exactly, according
to the Newtonian law of the inverse square. The minute differences
between the effects deduced from his theory and those deduced from
Newton are measurable in certain cases. There are, so far, three
crucial tests of the relative accuracy of the new theory and the old.

(1) The perihelion of Mercury shows a discrepancy which has long
puzzled astronomers. This discrepancy is fully accounted for by
Einstein. At the time when he published his theory, this was its only
experimental verification.

(2) Modern physicists were willing to suppose that light might be
subject to gravitation--i.e., that a ray of light passing near a
great mass like the sun might be deflected to the extent to which a
particle moving with the same velocity would be deflected according