Page:The Meaning of Relativity - Albert Einstein (1922).djvu/36

24 $$\mathbf{i}$$ 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 $$\mathbf{e}$$ is also to be regarded as a vector. Then $$\mathbf{h}$$ cannot be regarded as a vector. The equations may, however, easily be interpreted if $$\mathbf{h}$$ is regarded as a symmetrical tensor of the second rank. In this sense, we write $$h_{23},h_{31},h_{12}$$ in place of $$h_1,h_2,h_3$$ respectively. Paying attention to the skew-symmetry of $$h_{\mu\nu}$$, the first three equations of (19) and (20) may be written in the form

In contrast to $$\mathbf{e}$$, $$\mathbf{h}$$ 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