, are components of a co-variant vector, which, with the co-ordinate differentials, form the scalar
; we see from this example how natural is the definition of the co-variant vectors.
There are here, also, tensors of any rank, which may have co-variant or contra-variant character with respect to each index; as with vectors, the character is designated by the position of the index. For example,
denotes a tensor of the second rank, which is co-variant with respect to the index
, and contra-variant with respect to the index
