_dx₁_/_ds_, _dx₂_/_ds_, _dx₃_/_ds_, can take any values. This signifies that any velocity _v_ = √((_dx₁_/_dx₄_)² + (_dx₂_/_dx₄_)² + (_dx₃_/_dx₄_)²) can appear which is less than the velocity of light in vacuum (_v_ < 1). If we finally limit ourselves to the consideration of the case when _v_ is small compared to the velocity of light, it signifies that the components _dx₁_/_ds_, _dx₂_/_ds_, _dx₃_/_ds_, can be treated as small quantities, whereas _dx₄_/_ds_ is equal to 1, up to the second-order magnitudes (the second point of view for approximation). Now we see that, according to the first view of approximation, the magnitudes γ_{μν}^τ’s are all small quantities of at least the first order. A glance at (46) will also show, that in this equation according to the second view of approximation, we are only to take into account those terms for which μ = ν = 4. By limiting ourselves only to terms of the lowest order we get instead of (46), first, the equations:— _d²__x__{τ}/_dt²_ = Γ₄₄^τ, where _ds_ = _dx₄_ = _dt_, or by limiting ourselves only to those terms which according to the first stand-point are approximations of the first order, It must be admitted, that this introduction of the energy-tensor of matter cannot be justified by means of the Relativity-Postulate alone; for we have in the foregoing analysis deduced it from the condition that the energy of the gravitation-field should exert gravitating action in the same way as every other kind of energy. The strongest ground for the choice of the above equation however lies in this, that they lead, as their consequences, to equations expressing the conservation of the components of total energy (the impulses and the energy) which exactly correspond to the equations (49) and (49a). This shall be shown afterwards. §17. The laws of conservation in the general case. The equations (52) can be easily so transformed that the second member on the right-hand side vanishes. We reduce (52) with reference to the indices μ and σ and subtract the equation so obtained after multiplication with ½ δ_{μ}^σ from (52). We obtain, (52a) ∂/∂_x__{α}(_g_^{σβ} Γ_{μβ}^α - ½ δ_{μ}^σ _g_^{λβ} Γ_{λβ}^α) = -κ(_t__{μ}^σ + T_{μ}^σ) we operate on it by ∂/∂_x__{σ}. Now, ∂²/∂_x__{α}∂_x__{σ} (_g_^{σβ}Γ_{μβ}^α) = -½ ∂²/∂_x__{α}∂_x__{σ} [_g_^{σβ} _g_^{αλ}(∂_g__{μλ}/∂_x__{β} + ∂_g__{βλ}/∂_x__{μ} - ∂_g__{μβ}/∂_x__{λ})]. The first and the third member of the round bracket lead to expressions which cancel one another, as can be easily seen by interchanging the summation-indices α, and σ, on the one hand, and β and λ, on the other. The second term can be transformed according to (31). So that we get, (54) ∂²/∂_x__{α}∂_x__{σ} (_g_^{σβ}γ_{μβ}^α) = ½ ∂³_g_^{αβ}/∂_x__{σ}∂_x__{β}∂_x__{μ} The second member of the expression on the left-hand side of (52a) leads first to