can easily be transferred to any other axis when the system of axes are subjected to a transformation about this last axis. So we came to a more general law: —

Let be a vector with the components , and let . By we shall denote any vector which is perpendicular to , and by , we shall denote components of in direction of and .

Instead of *x, y, z, t*, new magnetudes *x,' y,' z,' t'* will be introduced in the following way. If for the sake of shortness, is written for the vector with the components *x, y, z* in the first system of reference, for the same vector with the components *x', y', z'* in the second system of reference, then *for the direction of* we have

(10) | , |

*and for every perpendicular direction*

(11) | , |

*and further*

(12) |

The notations and are to be understood in the sense that with the directions , and every direction perpendicular to in the system *x, y, z* are always associated the directions with the same direction cosines in the system *x', y', z'* ,

A transformation which is accomplished by means of (10), (11), (12) with the condition will be called a *special Lorentz-transformation*. We shall call the *vector*, the direction of the axis, and the magnitude of the *moment* of this transformation.

*If further and the vectors , in the system* x', y', z' *are so defined that,*

(13) | , |