the surface 26 to be hardened and by the walls of the peening chamber 10 in addition the balls 18 collide with one another as a result of the random scattering of the balls 18 a homogenous treatment of the surface 26 to be hardened is achieved fig3 shows a schematic representation of a cross section according to fig2 through an apparatus for implementing the inventive method contrary to fig2 the drive pinion 12 is shown in fig3 in a radial cross section in other words in a cross section at right angles to the rotational axis 13 the view of the remaining parts in fig3 can essentially correspond to the cross section shown in fig2 with only the part 11 and or 12 to be hardened being arranged differently alternatively the cross section shown in fig3 in respect of all parts may be a cross section at right angles to the cross section shown in fig2 the longitudinal axis of the apparatus is identified in both fig2 and 3 with reference character 15 the teeth 24 of the drive pinion 12 shown in fig3 include tooth flanks 25 with the aid of the inventive method the tooth flanks 25 can in particular be effectively hardened since as a result of the random scattering of the balls the whole surface to be hardened can be evenly treated fig4 and 5 show a cross section through part of an apparatus for implementing the inventive method fig4 and 5 show the hardening of the inner bearing surface 21 of a roller bearing.