Page:Grundgleichungen (Minkowski).djvu/19

 (2) Further relations, which characterise the influence of existing matter for the most important case to which we limit ourselves, i.e. for isotopic bodies; — they are comprised in the equations

where $$\epsilon$$ = dielectric constant, $$\mu$$ = magnetic permeability, $$\sigma$$ = the conductivity of matter, all given as function of x, y, z, t. $$\mathfrak{s}$$ is here the conduction current.

By employing a modified form of writing, I shall now cause a latent symmetry in these equations to appear. I put, as in the previous work,

$$x_{1} = x,\ x_{2} = y,\ x_{3} =z,\ x_{4} = it$$

and write $$s_{1},\ s_{2},\ s_{3},\ s_{4}$$ for $$\mathfrak{s}_{x},\ \mathfrak{s}_{y},\ \mathfrak{s}_{z},\ i\varrho$$,

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

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

and $$F_{23},\ F_{31},\ F_{12},\ F_{14},\ F_{24},\ F_{34}$$

for $$\mathfrak{M}_{x},\ \mathfrak{M}_{y},\ \mathfrak{M}_{z},\ -i\mathfrak{E}_{x},\ i\mathfrak{E}_{y},\ i\mathfrak{E}_{z}$$;

lastly we shall have the relation $$f_{kh} = -f_{hk},\ F_{kh} = -F_{hk}$$, (the letter f, F shall denote the field, s the (i.e. current).

Then the fundamental Equations can be written as