It is shown that a suitable set of Cauchy’s conditions for Einstein’s equations in vacuo consists in specifying the values ofgkl andgkl,0 on a hypersurfacex0 = 0. The correspondingg0k are to be found by solving threespatial second order differential equations, andg00 is then given by analgebraic relation. The first and higher time derivatives ofg0μ remain completely undetermined by the field equations, thus leaving room for arbitrary coordinate transformations. It is further shown that even if thegkl are chosen close to their Galilean values, and if thegkl,0 are small, the remainingg0ν will in general not be close to their Galilean values. However, a detailed investigation of the physical components of the curvature tensor shows that the field can nevertheless be weak, thus implying that the large discrepancies between theg0μ and their Galilean values are only a coordinate effect. The field is really strong only close to domains where the determinant of theg0ν vanishes. By a suitable coordinate transformation, those domains can be made to shrink to points, and the resulting singularities may be interpreted as representing matter. This supports Einstein’s view that matter should not be considered as something foreign to the metric field itself.