Fig. 5.
He calls Euclidean geometry parabolic ([Fig. 5]), for the branches of a parabola continue to recede from one to another, and yet in order to obtain consistent results in its formulæ we are obliged only to assign one point at infinity to it, just as to the Euclidean straight line. Lobatschewsky's geometry is similarly called hyperbolic ([Fig. 5]), since a hyperbola has two points at infinity, corresponding in analogy to the two points at infinity at which the two parallels through a point external to a straight line cut the latter.
The fact that one is obliged to renounce Euclidean geometry in the general theory of relativity leads to the conclusion that our space is to be regarded as finite but unbounded: it is curved, as Einstein expresses it, like the faintest of ripples on a surface of water.
[SOME ASPECTS OF RELATIVITY]
BY HENRY L. BROSE, M.A.
UP to the present, three methods of verifying Einstein's Theory of Relativity have been suggested.
The first one, which was a direct outcome of the new gravitational field-equations proposed by Einstein, proved successful. The slow motion of Mercury's perihelion which long mystified astronomers was immediately accounted for. This result is the more remarkable as all other explanations of this phenomena were artificial in origin, consisting of a hypothesis formulated ad hoc which could not be verified by observation.
The second method involved the deflection of a ray of light in its passage through a varying gravitational field. The results of the total eclipse of the sun which occurred on 29th May, 1919, have become famous and were recorded as confirming Einstein's prediction. The results of a more recent expedition have proved finally conclusive.