(87) ω (S - Ṡ) = (εμ - 1) Ω When the matter is at rest at a space-time point, ω = 0, then the equation 86) denotes the existence of the following equations Z_{_y_} = Y_{_z_}, X_{_z_} = Z_{_x_}, Y_{_x_} = X_{_y_}, and from 83), T_{_x_} = Ω₁, T_{_y_} = Ω₂, T_{_z_} = Ω₃ X_{_t_} = εμΩ₁, Y_{_t_} = εμΩ₂, Z_{_t_} = εμΩ₃ Now by means of a rotation of the space co-ordinate system round the null-point, we can make, Z_{_y_} = Y_{_z_} = 0, X_{_z_} = Z_{_x_} = 0, X_{_x_} = X_{_y_} = 0, According to 71), we have (88) X_{_x_} + Y_{_y_} + Z_{_z_} + T_{_t_} = 0, and according to 83), T_{_t_} > 0. In special cases, where ω vanishes it follows from 81) that X_{_x_}² = Y_{_y_}² = Z_{_z_}² = T_{_t_}², = (Det^{1/4} S)², and if T, and one of the three magnitudes X_{_x_}, Y_{_y_}, Z_{_z_} are = ±Det^{1/4} S, the two others = -Det^{1/4} S. If Ω does not vanish let Ω ≠ 0, then we have in particular from 80) T_{_z_} X_{_t_} = 0, T_{_z_} Y_{_t_} = 0, Z_{_z_} T_{_z_} + T_{_z_} T_{_t_} = 0, and if Ω₁ = 0, Ω₂ = 0, Z_{_z_} = -T_{_t_} It follows from (81), (see also 83) that X_{_x_} = -Y_{_y_} = ±Det^{1/4} S, and -Z_{_z_} = T_{_t_} = √(Det^{½} S + εμΩ₃²) > Det^{1/4}S. The space-time vector of the first kind (89) K = lor S, is of very great importance for which we now want to demonstrate a very important transformation According to 78), S = L + _f_F, and it follows that lor S = lor L + lor _f_F. The symbol ‘lor’ denotes a differential process which in lor _f_F, operates on the one hand upon the components of _f_, on the other hand also upon the components of F. Accordingly lor _f_F can be expressed as the sum of two parts. The first part is the product of the matrices (lor _f_) F, lor _f_ being regarded as a 1 × 4 series matrix. The second part is that part of lor _f_F, in which the diffentiations operate upon the components of F alone. From 78) we obtain _f_F = -F*_f_* - 2L; hence the second part of lor _f_F = -(lor F*)_f_* + the part of -2 lor L, in which the differentiations operate upon the components of F alone. We thus obtain lor S = (lor _f_)F - (lor F*)_f_* + N, where N is the vector with the components N_{_h_} = ½(∂_f₂₃_/∂_x__{_h_} F₂₃ + ∂_f₃₁_/∂_x__{_h_} F₃₁ + ∂_f₁₂_/∂_x__{_h_} F₁₂ + ∂_f₁₄_/∂_x__{_h_} F₁₄ + ∂_f₂₄_/∂_x__{_h_} F₂₄ + ∂_f₃₄_/∂_x__{_h_} F₃₄ - ∂F₂₃/∂_x__{_h_} _f₂₃_ - ∂F₃₁/∂_x__{_h_} _f_₃₁ - ∂F₁₂/∂_x__{_h_} _f₁₂_ - ∂F₁₄/∂_x__{_h_} _f₁₄_ - ∂F₂₄/∂_x__{_h_} _f₂₄_ - ∂F₃₄/∂_x__{_h_} _f₃₄_), (_h_ = 1, 2, 3, 4) By using the fundamental relations A) and B), 90) is transformed into the fundamental relation (91) lor S = -_s_F + N. In the limitting case ε = 1, μ = 1, _f_ = F, N vanishes identically.