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/2r.
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.