# Page:AbrahamMinkowski1.djvu/11

where under ${\displaystyle {\mathfrak {W}}}$ we have to understand the vector

 (22) ${\displaystyle {\mathfrak {W=[DB]}}-c{\mathfrak {g}}}$

Now, we pass to the discussion of special theories, where we confine ourselves to isotropic bodies throughout.

§ 6. Theory of H. Hertz.

Hertz's electrodynamics of moving bodies sets the vectors ${\displaystyle {\mathfrak {D}}}$ and ${\displaystyle {\mathfrak {B}}}$ proportional to ${\displaystyle {\mathfrak {E'}}}$ and ${\displaystyle {\mathfrak {H'}}}$

 (23) ${\displaystyle {\mathfrak {D}}=\epsilon {\mathfrak {E}}',\ {\mathfrak {B}}=\mu {\mathfrak {H}}'}$

Accordingly,

${\displaystyle {\mathfrak {E'{\dot {D}}-D{\dot {E}}'}}=0,\ {\mathfrak {H'{\dot {B}}-B{\dot {H}}'}}=0}$

where ${\displaystyle \epsilon }$ and ${\displaystyle \mu }$ are considered as constants for a certain material point of a moving body.

Thus it follows from (18)

 (24) ${\displaystyle {\mathfrak {g}}=0}$

Hertz's theory doesn't know the concept of electromagnetic momentum. It derives the ponderomotive force from the stresses alone, where it is irrelevant according to (10), whether one relates the stresses to stationary or to co-moving surfaces. A torque of the relative stresses doesn't arise, and also both sides of (18a) are equal to zero.

The energy density has a value according to (19)

 (25) ${\displaystyle \psi ={\frac {1}{2}}\epsilon {\mathfrak {E}}'^{2}+{\frac {1}{2}}\mu {\mathfrak {H}}'^{2}}$

The simple approach, by which Hertz's theory connects the excitations ${\displaystyle {\mathfrak {DB}}}$ with the electromagnetic forces ${\displaystyle {\mathfrak {E'H'}}}$, was, however, not confirmed by experiment as mentioned above. Thus only the choice between the theories to be discussed in the following paragraphs, remain.

§ 7. Theory of E. Cohn.

E. Cohn based the electrodynamics of moving bodies on the following connecting equations

 (26) ${\displaystyle {\begin{cases}{\mathfrak {D}}=\epsilon {\mathfrak {E}}'-[{\mathfrak {qH}}'],\\{\mathfrak {B}}=\mu {\mathfrak {H}}'-[{\mathfrak {qE}}'].\end{cases}}}$