Page:Grundgleichungen (Minkowski).djvu/6

 i.e. the components of the convection current $$\varrho\mathfrak{w}$$, and the electric density multiplied by $$\sqrt{-1}$$.

Further I shall write

$$f_{23},\ f_{31},\ f_{12},\ f_{14},\ f_{24},\ f_{34}$$

for

$$\mathfrak{m}_{x},\ \mathfrak{m}_{y},\ \mathfrak{m}_{z},\ -i\mathfrak{e}_{x},\ -i\mathfrak{e}_{y},\ -i\mathfrak{e}_{z}$$,

i.e., the components of $$\mathfrak{m}$$ and $$-i\mathfrak{e}$$ along the three axes; now if we take any two indices h, k out of the series

$$f_{kh} = -f_{hk}$$,

therefore

Then the three equations comprised in (I), and the equation (II) multiplied by i becomes

On the other hand, the three equations comprised in (III) multiplied by -i, and equation (IV) multiplied by -1, become

By means of this method of writing we at once notice the perfect symmetry of the 1st as well as the 2nd system of equations