Page:Grundgleichungen (Minkowski).djvu/9

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(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)

  1. 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