is zero or has a non-vanishing value, we obtain the infinite universe, or the finite universe of either de Sitter or Einstein. In particular, Einstein’s universe will be the outcome if we impose the condition of stability upon the universe. We see, therefore, that the principle of action proves that all three types of universe are possible. If we wish to decide which type corresponds to the real universe, we must take other facts into consideration, as was explained in the chapter on the finiteness of the universe.
Now there remains one other important point which we must mention before abandoning the discussion of the law of gravitation. We saw that the principle of action alone did not enable us to decide whether the constant
, which was adjoined to the action
of the metrical field, was zero or had some non-vanishing value. In other words, it did not enable us to decide whether the universe was infinite or finite. But this is not the only source of indeterminateness. We mentioned that Einstein chose
for the function of action of the metrical field because it was the simplest possible invariant made up of
