more complicated value and this is supplied to the comparator the latter compares the value set on the input device 48 for the desired value and the tolerance with the actual value and in the case of approximation or exceeding via the release mechanism 49 e g a triac or relay initiates a readjustment movement on the part of the readjusting device normally a stepwise setting is sufficient because a single readjusting step is normally sufficient for several bores if the measuring device were fitted in the vicinity of guide zone 35 or at another point on this side of the working area then the measurement could be performed directly following the forward stroke of the work cycle or also during a levelling stroke the measuring device can also be provided for checking the pre worked workpieces in that in a manner not shown in the drawing the measuring mechanism 35 which also contains a switching device for the release of measuring air adapted to the working cycle is connected with an additional device which switches in the air supply when the tool enters the unmachined bore if the measuring tool establishes a considerable undersize the machining operation can be.