(54)
|
|
The vector
is perpendicular to w; we can call it the Magnetic rest-force.
Relations analogous to these hold among the quantities
and Relation (D) can be replaced by the formula
{D}
|
|
We can use the relations (C) and (D) to calculate F and f from
and
, we have
and applying the relation (45) and (46), we have
(55)
|
,
|
(56)
|
,
|
i.e.
|
, etc.
, etc.
|
Let us now consider the space-time vector of the second kind
, with the components
|
,
,
|
Then the corresponding space-time vector of the first kind
vanishes identically owing to equations 49) and 53).
Let us now take the vector of the 1st kind
(57)
|
|
with the components
![{\displaystyle \Omega _{1}=-i\left|{\begin{array}{ccc}w_{2},&w_{3},&w_{4}\\\Phi _{2},&\Phi _{3},&\Phi _{4}\\\Psi _{2},&\Psi _{3},&\Psi _{4}\end{array}}\right|}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d98aa974119ad6054b3f4de65ee38644df1407dc)
, etc.
Then by applying rule (45), we have