*The space-time vector of the first kind*

(89) |

*is of very great importance* for which we now want to demonstrate a very important transformation

According to 78), , and it follows that

The symbol *lor* denotes a differential process which in *lor fF*, operates on the one hand upon the components of *f*, on the other hand also upon the components of *F*. Accordingly *lor fF* can be expressed as the sum of two parts. The first part is the product of the matrices *(lor f)F*, *lor f* being regarded as a 1✕4 series matrix. The second part is that part of *lor fF*, in which the diffentiations operate upon the components of *F* alone. From 78) we obtain

hence the second part of *lor fF* = the part of , in which the differentiations operate upon the components of *F* alone. We thus obtain

(90) | , |

where *N* is the vector with the components

By using the fundamental relations A) and B), 90) is transformed into the *fundamental relation*

(91) |

In the limitting case , *N* vanishes identically.

Now upon the basis of the equations (55) and (56), and referring back to the expression (82) for *L*, and from 57) we obtain the following expressions as components of *N*,—