I enunciate in the following manner the general theorem of relativity corresponding to the equations (I)-(iv),—which are the fundamental equations for Äther. If _x_, _y_, _z_, _it_ (space co-ordinates, and time _it_) is subjected to a Lorentz transformation, and at the same time (_pu__{_x_}, _pu__{_y_}, _pu__{_z_}, _i_ρ) (convection-current, and charge density ρ_i_) is transformed as a space time vector of the 1st kind, further (_m__{_x_}, _m__{_y_}, _m__{_z_}, -_ie__{_x_}, -_ie__{_y_}, -_ie__{_z_}) (magnetic force, and electric induction × (-_i_) is transformed as a space time vector of the 2nd kind, then the system of equations (I), (II), and the system of equations (III), (IV) transforms into essentially corresponding relations between the corresponding magnitudes newly introduced into the system. These facts can be more concisely expressed in these words: the system of equations (I and II) as well as the system of equations (III) (IV) are covariant in all cases of Lorentz-transformation, where (ρ_u_, _i_ρ) is to be transformed as a space time vector of the 1st kind, (_m_ - _ie_) is to be treated as a vector of the 2nd kind, or more significantly,— (ρ_u_, _i_ρ) is a space time vector of the 1st kind, (_m_ - _ie_)[17] is a space-time vector of the 2nd kind. I shall add a few more remarks here in order to elucidate the conception of space-time vector of the 2nd kind. Clearly, the following are invariants for such a vector when subjected to a group of Lorentz transformation. (_i_) _m²_ - _e²_ = _f₂₃²_ + _f₃₁²_ + _f₁₂²_ + _f₁₄²_ + _f₂₄²_ + _f₂₄²_ _me_ = _i_(_f₂₃__f₁₄_ + _f₃₁__f₂₄_ + _f₁₂__f₃₄_). A space-time vector of the second kind (_m_ - _ie_), where (_m_ and _e_) are real magnitudes, may be called singular, when the scalar square (_m_ - _ie_)² = 0, _ie_ _m²_ - _e²_ = 0, and at the same time (_m e_) = 0, _ie_ the vector _m_ and _e_ are equal and perpendicular to each other; when such is the case, these two properties remain conserved for the space-time vector of the 2nd kind in every Lorentz-transformation. If the space-time vector of the 2nd kind is not singular, we rotate the spacial co-ordinate system in such a manner that the vector-product [_me_] coincides with the Z-axis, _i.e._ _m__{_x_} = 0, _e__{_x_} = 0. Then (_m__{_x_}, -_i e__{_x_})² + (_m__{_y_}, -_i e__{_y_})² ≠ 0. Therefore (_e__{_y_} + _i m__{_y_})/(_e__{_x_} + _i e__{_x_}) is different from +_i_, and we can therefore define a complex argument (φ + _i_ψ) in such a manner that tan (φ + _i_ψ) _e__{_y_} + _i m__{_y_} = ------------------------- _e__{_x_} + _i m__{_x_}