For this matrix I shall use the *shortened from* lor.

Then if *S* is, as in (62), a space-time matrix of the II. kind, by *lor S'* will be understood the 1✕4 series matrix

where

(64) |

When by a Lorentz transformation , a new reference system is introduced, we can use the operator

Then *S* is transformed to , so by *lor' S*is meant the 1✕4 series matrix, whose element are

Now for the differentiation of any function of (*x y z t*) we have the rule

, |

so that, we have symbolically

Therefore it follows that

(65) | , |

*i.e.*, *lor S* *behaves like a space-time vector of the first kind.*

If *L* is a multiple of the unit matrix, then by *lor L* will be denoted the *matrix with the elements*