If then, by referring back to equations (9), we carry out the transformation (1) through the angle ψ and a subsequent rotation round the Z-axis through the angle φ, we perform a Lorentz-transformation at the end of which _m__{_y_} = 0, _e__{_y_} = 0, and therefore _m_ and _e_ shall both coincide with the new Z-axis. Then by means of the invariants _m²_ - _e²_, (_me_) the final values of these vectors, whether they are of the same or of opposite directions, or whether one of them is equal to zero, would be at once settled. § 6. Concept of Time. By the Lorentz transformation, we are allowed to effect certain _changes_ of the time parameter. In consequence of this fact, it is no longer permissible to speak of the absolute simultaneity of two events. The ordinary idea of simultaneity rather presupposes that six independent parameters, which are evidently required for defining a system of space and time axes, are somehow reduced to three. Since we are accustomed to consider that these limitations represent in a unique way the actual facts very approximately, we maintain that the simultaneity of two events exists of themselves.[18] In fact, the following considerations will prove conclusive. Let a reference system (_x_, _y_, _z_, _t_) for space time points (events) be somehow known. Now if a space point A (_x₀_, _y₀_, _z₀_) the time _t₀_ be compared with a space point P (_x_, _y_, _z_) at the time _t_, and if the difference of time _t_ - _t₀_, (let _t_ > _t₀_) be less than the length A P _i.e._ less than the time required for the propagation of light from A to P, and if _q_ = (_t_ - _t₀_)/(A P) < 1, then by a special Lorentz transformation, in which A P is taken as the axis, and which has the moment _q_, we can introduce a time parameter _t′_, which (see equation 11, 12, § 4) has got the same value _t′_ = _0_ for both space-time points (A, _t₀_), and (P, t). So the two events can now be comprehended to be simultaneous. Further, let us take at the same time _t₀_ = 0, two different space-points A, B, or three space-points (A, B, C) which are not in the same space-line, and compare therewith a space point P, which is outside the line A B, or the plane A B C, at another time _t_, and let the time difference _t_ - _t₀_ (t > _t₀_) be less than the time which light requires for propagation from the line A B, or the plane (A B C) to P. Let q be the quotient of (_t_ - _t₀_) by the second time. Then if a Lorentz transformation is taken in which the perpendicular from P on A B, or from P on the plane A B C is the axis, and q is the moment, then all the three (or four) events (A, _t₀_), (B, _t₀_), (C, _t₀_) and (P, t) are simultaneous. If four space-points, which do not lie in one plane, are conceived to be at the same time _t₀_, then it is no longer permissible to make a change of the time parameter by a Lorentz-transformation, without at the same time destroying the character of the simultaneity of these four space points.