$S{\bar {S}}=\leftS_{hk}S_{kh}\right$
an alternating matrix, and denotes a spacetime vector of the second kind. From the expressions (83), we obtain,
(85) 
$S{\bar {S}}=(\epsilon \mu 1)[w,\Omega ],$ 
from which we deduce that [see (57), (58)].
(86) 
$w(S{\bar {S}})^{*}=0$, 
(87) 
$w(S{\bar {S}})=(\epsilon \mu 1)\Omega$, 
When the matter is at rest at a spacetime point, ${\mathfrak {w}}=0$, then the equation 86) denotes the existence of the following equations
$Z_{y}=Y_{z},\ X_{z}=Z_{x},\ Y_{x}=X_{y}$;
and from 83),

$T_{x}=\Omega _{1},\ T_{y}=\Omega _{2},\ T_{z}=\Omega _{3}$
$X_{t}=\epsilon \mu \Omega _{1},\ Y_{t}=\epsilon \mu \Omega _{2},\ Z_{t}=\epsilon \mu \Omega _{3}$

Now by means of a rotation of the space coordinate system round the nullpoint, we can make,
$Z_{y}=Y_{z}=0,\ X_{z}=Z_{x}=0,\ Y_{x}=X_{y}=0$;
According to 71), we have
(88) 
$X_{x}+Y_{y}+Z_{z}+T_{t}=0$ 
and according to 83), $T_{t}>0$. In special eases, where $\Omega$ vanishes it follows from 81) that
$X_{x}^{2}=Y_{y}^{2}=Z_{z}^{2}=T_{t}^{2}=(Det^{\frac {1}{4}}S)^{2}$
and if $T_{t}$ and one of the three magnitudes $X_{x},\ Y_{y},\ Z_{z}$ are $=+Det^{\frac {1}{4}}S$, the two others $=Det^{\frac {1}{4}}S$. If $\Omega$ does not vanish let $\Omega _{3}\neq 0$, then we have in particular from 80)
$T_{z}X_{t}=0,\ T_{z}Y_{t}=0,\ Z_{z}T_{z}+T_{z}Z_{t}=0$
and if $\Omega _{1}=0,\ \Omega _{1}=0,\ Z_{z}=T_{t}$. It follows from (81), (see also 88) that

$X_{x}=Y_{y}=\pm Det^{\frac {1}{4}}S$,
$Z_{z}=T_{t}={\sqrt {Det^{\frac {1}{2}}S+\epsilon \mu \Omega _{2}^{2}}}>Det^{\frac {1}{4}}S$.
