room temperature i e at approx 21 u00b0 c the mechanical loading can heat the abrasive liquid to approx 25 u00b0 c which however has no adverse effect on the material removal rate the delivery line 14 leads into the interior of the vessel 11 where the water 3 is accelerated to approx 40 m s using a nozzle 9 the nozzle 9 is directed onto the surface s which moves with the holding apparatus 10 beneath it in a pressurized tank 13 there is air 4 which can be introduced into the water 3 via a connection line 16 the supply of air is varied by means of a valve 8 the higher the desired material removal rate the more air 4 is added to the water 3 the maximum air content in the water 3 is 70 of the total volume the pressure in the tank 13 is 250 bar the air 4 is supplied at a pressure of 14 to 50 bar what is important in this context is for the feed pressure of the air to be greater than the delivery pressure of the water for polishing the air supply is suppressed or at least reduced the water 3 used is passed back into the tank 12 via a discharge 15 the abrasive particles 5 are therefore in a closed circuit indicated by the arrows 6 this keeps the consumption of material as low as possible the air supply is calibrated on a reference workpiece not shown the material removal rate for the workpiece 2 can then be set as required on the basis of this calibration an alternative embodiment of the apparatus 1 according to the invention is illustrated in fig2 as in the exemplary embodiment shown in fig1 the abrasive liquid 3.