-K/_c²_ ∫ρ_d_τ/_r_, where K denotes usually the gravitation-constant. 6.7 x 10⁻⁸; equating them we get (69) κ = 8πK/_c²_ = 1.87 x 10⁻²⁷. §22. Behaviour of measuring rods and clocks in a statical gravitation-field. Curvature of light-rays. Perihelion-motion of the paths of the Planets. In order to obtain Newton’s theory as a first approximation we had to calculate only _g₄₄_, out of the 10 components _g__{μν} of the gravitation-potential, for that is the only component which comes in the first approximate equations of motion of a material point in a gravitational field. We see however, that the other components of _g__{μν} should also differ from the values given in (4) as required by the condition _g_ = -1. For a heavy particle at the origin of co-ordinates and generating the gravitational field, we get as a first approximation the symmetrical solution of the equation:— { _g__{ρσ} = -δ_{ρσ} - α(_x__{ρ} _x__{σ})/_r³_ (ρ and σ 1, 2, 3) { (70) { _g__{ρ4} = _g__{4ρ} = 0 (ρ 1, 2, 3) { { _g₄₄_ = 1 - α/_r_. δ_{ρσ} is 1 or 0, according as ρ = σ or not and _r_ is the quantity +√(_x₁²_ + _x₂²_ + _x₃²_). On account of (68a) we have (70a) α = κM/4π where M denotes the mass generating the field. It is easy to verify that this solution satisfies approximately the field-equation outside the mass M. Let us now investigate the influences which the field of mass M will have upon the metrical properties of the field. Between the lengths and times measured locally on the one hand, and the differences in co-ordinates _dx__{ν} on the other, we have the relation _ds²_ = _g__{μν} _dx__{μ} _dx__{ν}. For a unit measuring rod, for example, placed parallel to the _x_ axis, we have to put _ds²_ = -1, _dx₂_ = _dx₃_ = _dx₄_ = 0 then -1 = _g_₁₁_dx₁²_. If the unit measuring rod lies on the _x_ axis, the first of the equations (70) gives _g₁₁_ = -(1 + α/_r_). From both these relations it follows as a first approximation that (71) _dx_ = 1 - α/2_r_. The unit measuring rod appears, when referred to the co-ordinate-system, shortened by the calculated magnitude through the presence of the gravitational field, when we place it radially in the field. Similarly we can get its co-ordinate-length in a tangential position, if we put for example _ds²_ = -1, _dx₁_ = _dx₃_ = _dx₄_ = 0, _x₁_ = _r_, _x₂_ = _x₃_ = 0 we then get (71a) -1 = _g₂₂_ _dx₂²_ = -_dx₂²_. The gravitational field has no influence upon the length of the rod, when we put it tangentially in the field.