there are no frictional forces present, from which it follows that = . If only is different from zero, let , by which is determined. We then obtain for the complete stress tensor, [Pg 22] The heuristic value of the theory of invariants, which arises from the isotropy of space (equivalence of all directions), becomes evident from this example. We consider, finally, Maxwell's equations in the form which are the foundation of the electron theory of Lorentz. is a vector, because the current density is defined as the density of electricity multiplied by the vector velocity of the electricity. According to the first three equations it is evident that is also to be regarded as a vector. Then cannot be regarded as a vector.[6] The equations may, however, easily be [Pg 23] interpreted if is regarded as a skew-symmetrical tensor of the second rank. In this sense, we write , , in place of , , respectively. Paying attention to the skew-symmetry of , the first three equations of (19) and (20) may be written in the form In contrast to , appears as a quantity which has the same type of symmetry as an angular velocity. The divergence equations then take the form The last equation is a skew-symmetrical tensor equation of the third rank (the skew-symmetry of the left-hand side with respect to every pair of indices may easily be proved, if attention is paid to the skew-symmetry of ). This notation is more natural than the usual one, because, in contrast to the latter, it is applicable to Cartesian left-handed systems as well as to right-handed systems without change of sign. [Pg 24] [6]These considerations will make the reader familiar with tensor operations without the special difficulties of the four-dimensional treatment; corresponding considerations in the theory of special relativity (Minkowski's interpretation of the field) will then offer fewer difficulties. LECTURE II THE THEORY OF SPECIAL RELATIVITY