I) curl _m_ - ∂_e_/∂_t_ = C₁, II) div _e_ = ρ III) curl E + ∂M/∂_t_ = 0 IV) div M = 0 The velocity of matter occurs only in the auxiliary equations which characterise the influence of matter on the basis of their characteristic constants ε, μ, σ. Let us now transform these auxiliary equations V′) into the original co-ordinates (_x_, _y_, _z_, and _t_.) According to formula 15) in § 4, the component of _e′_ in the direction of the vector _u_ is the same as that of (_e_ + [_u_ _m_]), the component of _m′_ is the same as that of _m_ - [_u_ _e_], but for the perpendicular direction _ū_, the components of _e′_, _m′_ are the same as those of (_e_ + [_u_ _m_]) and (_m_ - [_u_ _e_], multiplied by 1/√(1 - _u²_). On the other hand E′ and M′ shall stand to E + [_u_M], and M - [_u_E] in the same relation as _e′_ and _m′_ to _e_ + [_um_], and _m_ - (_ue_). From the relation _e′_ = εE′, the following equations follow (C) _e_ + [_um_] = ε(E + [_u_M]), and from the relation M′ = μ_m′_, we have (D) M - [_u_ E] = μ(_m_ - [_ue_]), For the components in the directions perpendicular to _u_, and to each other, the equations are to be multiplied by √(1 - _u²_). Then the following equations follow from the transformation? equations (12), (10), (11) in § 4, when we replace q, _r__{_v_}, _r__{_ṽ_}, _t_, _r′__{_v_}, _r′__{_ṽ_}, _t’_ by |_u_|, C_{_u_}, C_{_ū_}, ρ, C′_{_u_}, C′_{_ū_}, ρ′ ρ′ = (-|_u_| C_{_u_} + ρ)/√(1 - _u²_), C’_{_u_} = (C_{_u_} - |_u_|ρ)/√(1 - _u²_), C′_{_ū_} = C_{_ū_}, E) (C_{_u_} - |_u_|ρ)/√(1 - _u²_) = σ(E + [_u_M])_{_u_}, C_{_ū_} = σ (E + [_u_M])_{_u_}/√(1 - _u²_). In consideration of the manner in which σ enters into these relations, it will be convenient to call the vector C - ρ_u_ with the components C_{_u_} - ρ|_u_| in the direction of _u_, and C′_{_ū_} in the directions _ū_ perpendicular to _u_ the “Convection current.” This last vanishes for σ = 0. We remark that for ε = 1, μ = 1 the equations _e′_ = E′, _m′_ = M′ immediately lead to the equations _e_ = E, _m_ = M by means of a reciprocal Lorentz-transformation with -_u_ as vector; and for σ = 0, the equation C′ = 0 leads to C = ρ_u_; that the fundamental equations of Äther discussed in § 2 becomes in fact the limitting case of the equations obtained here with ε = 1, μ = 1, σ = 0. § 9. The Fundamental Equations in Lorentz’s Theory. Let us now see how far the fundamental equations assumed by Lorentz correspond to the Relativity postulate, as defined in §8. In the article on Electron-theory (Ency., Math., Wiss., Bd. V. 2, Art 14) Lorentz has given the fundamental equations for any possible, even magnetised bodies (see there page 209, Eqn XXX′, formula (14) on page 78 of the same (part). (III_a″_) Curl (H - [_u_E]) = J + _d_D/_dt_ + _u_ div D - curl [_u_D].