numbers which we have often mentioned constitute symmetrical second-order covariant tensors. The tensor nature of the
’s means nothing else than that the components of the
’s in our co-ordinate system vary according to the rules of tensors when we pass from one co-ordinate system to another. The
’s being second-order covariant tensors, we may infer that by combining them with two displacements, or vectors, of opposite nature (i.e., contravariant vectors), we shall obtain an invariant. It is for this reason that
yields an invariant,[90] which, as we know, is nothing but the square of the length