Note 91 — Chapter XXVI · TENSORS AND THE LAWS OF NATURE
Reading edition
It is customary to represent scalars by ordinary letters, and tensors of the first, second and third orders, and so on, by letters followed by indices equal in number to the order of the tensor. Thus, is a tensor of the second order, is one of the third order, and so on.
When we substitute for these indices all possible arrangements of the numbers from to , where represents the dimensions of our continuum, we obtain thereby the various components of our tensors.
Thus, in a space of two dimensions, the various components of are , , , , which reduce to , , , owing to the identity of and , the tensor being symmetrical.
In order to differentiate at a glance contravariant tensors from covariant ones, the indices are placed above the letter. For instance, is the contravariant form of , and is the mixed form. We see, then, that should really be written , since refers to a contravariant vector.