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

$f_{32}=f_{23},\ f_{13}=f_{31},\ f_{21}=f_{12}$,
$f_{41}=f_{14},\ f_{42}=f_{24},\ f_{43}=f_{34}$,

Then the three equations comprised in (I), and the equation (II) multiplied by i becomes
(A) 
${\begin{array}{ccccccccc}&&{\frac {\partial f_{12}}{\partial x_{2}}}&+&{\frac {\partial f_{13}}{\partial x_{3}}}&+&{\frac {\partial f_{14}}{\partial x_{4}}}&=&\varrho _{1},\\\\{\frac {\partial f_{21}}{\partial x_{1}}}&&&+&{\frac {\partial f_{23}}{\partial x_{3}}}&+&{\frac {\partial f_{24}}{\partial x_{4}}}&=&\varrho _{2},\\\\{\frac {\partial f_{31}}{\partial x_{1}}}&+&{\frac {\partial f_{32}}{\partial x_{2}}}&&&+&{\frac {\partial f_{34}}{\partial x_{4}}}&=&\varrho _{3},\\\\{\frac {\partial f_{41}}{\partial x_{1}}}&+&{\frac {\partial f_{42}}{\partial x_{2}}}&+&{\frac {\partial f_{43}}{\partial x_{3}}}&&&=&\varrho _{4}.\end{array}}$ 
On the other hand, the three equations comprised in (III) multiplied by i, and equation (IV) multiplied by 1, become
(B) 
${\begin{array}{ccccccccc}&&{\frac {\partial f_{34}}{\partial x_{2}}}&+&{\frac {\partial f_{42}}{\partial x_{3}}}&+&{\frac {\partial f_{23}}{\partial x_{4}}}&=&0,\\\\{\frac {\partial f_{43}}{\partial x_{1}}}&&&+&{\frac {\partial f_{14}}{\partial x_{3}}}&+&{\frac {\partial f_{31}}{\partial x_{4}}}&=&0,\\\\{\frac {\partial f_{24}}{\partial x_{1}}}&+&{\frac {\partial f_{41}}{\partial x_{2}}}&&&+&{\frac {\partial f_{12}}{\partial x_{4}}}&=&0,\\\\{\frac {\partial f_{32}}{\partial x_{1}}}&+&{\frac {\partial f_{13}}{\partial x_{2}}}&+&{\frac {\partial f_{21}}{\partial x_{3}}}&&&=&0.\end{array}}$ 
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