(6) |

and

(7) | ^{[1]} |

Then we have for these newly introduced vectors with components ; and the quantity a series of equations I'), II'), III'), IV) which are obtained from I), II), III), IV) by simply dashing the symbols.

We remark here that e are components of the vector , where is a vector in the direction of the positive *z*-axis, and , and is the vector product of and ; similarly are the components of the vector .

The equations 6) and 7), as they stand in pairs, can be expressed as.

,
, |

If denotes any other real angle, we can form the following combinations : —

(8) |
, |

(9) |

### § 4. Special Lorentz-Transformation.

The role which is played by the *z*-axis in the transformation (4)

- ↑ The equations (5) are written in a different order, however, equations (6) and (7) in the same order as the equations mentioned before, which amounts to them