The dashed system has got the same meaning for the velocity _u′_ after the transformation as the first system of values has got for _u_ before transformation. If in particular the vector _v_ of the special Lorentz-transformation be equal to the velocity vector _u_ of matter at the space-time point (_x₁_, _x₂_, _x₃_, _x₄_) then it follows out of (10), (11), (12) that ω₁′ = 0, ω₂′ = 0, ω₃′ = 0, ω₄′ = _i_ Under these circumstances therefore, the corresponding space-time point has the velocity _v′_ = 0 after the transformation, it is as if we transform to rest. We may call the invariant ρ√(1 - _u²_) the rest-density of Electricity.[16] § 5. Space-time Vectors. Of the 1st and 2nd kind. If we take the principal result of the Lorentz transformation together with the fact that the system (A) as well as the system (B) is covariant with respect to a rotation of the coordinate-system round the null point, we obtain the general _relativity theorem_. In order to make the facts easily comprehensible, it may be more convenient to define a series of expressions, for the purpose of expressing the ideas in a concise form, while on the other hand I shall adhere to the practice of using complex magnitudes, in order to render certain symmetries quite evident. Let us take a linear homogeneous transformation, $$ \begin{vmatrix} x_{1} x_{2} x_{3} x_{4} \end{vmatrix} = \begin{vmatrix} a_{1 1} & a_{1 2} & a_{1 3} & a_{1 4} a_{2 1} & a_{2 2} & a_{2 3} & a_{2 4} a_{3 1} & a_{3 2} & a_{3 3} & a_{3 4} a_{4 1} & a_{4 2} & a_{4 3} & a_{4 4} \end{vmatrix} \begin{vmatrix} x_{1}' x_{2}' x_{3}' x_{4}' \end{vmatrix} $$ the Determinant of the matrix is +1, all co-efficients without the index 4 occurring once are real, while _a₄₁_, _a₄₂_, _a₄₃_, are purely imaginary, but _a₄₄_ is real and > 0, and _x₁²_ + _x₂²_ + _x₃²_ + _x₄²_ transforms into _x₁′²_ + _x₂′²_ + _x₃′²_ + _x₄′²_. The operation shall be called a general Lorentz transformation. (This notation, which is due to Dr. C. E. Cullis of the Calcutta University, has been used throughout instead of Minkowski’s notation, _x₁_ = _a₁₁x₁′_ + _a₁₂x₂′_+ _a₁₃x₃′_+ _a₁₄x₄′_.) If we put _x₁′_ = _x′_, _x₂′_ = _y′_, _x₃′_ = _z′_, _x₄′_ = _it′_, then immediately there occurs a homogeneous linear transformation of (_x_, _y_, _z_, _t_) to (_x′_, _y′_, _z′_, _t′_) with essentially real co-efficients, whereby the aggregate -_x²_ - _y²_ - _z²_ + _t²_ transforms into -_x′²_ - _y′²_ - _z′²_ + _t′²_, and to every such system of values _x_, _y_, _z_, _t_ with a positive _t_, for which this aggregate > 0, there always corresponds a positive _t’_; this last is quite evident from the continuity of the aggregate _x_, _y_, _z_, _t_. The last vertical column of co-efficients has to fulfil the condition 22) _a₁₄²_ + _a₂₄²_ + _a₃₄²_ + _a₄₄²_ = 1.