on the lines 56 and 60 respectively are each sent to a first input of respective serial digital adders 64 and 66 through respective lines 68 70 there arrive at the two respective second inputs of the adders 64 and 66 respective data u03b4 p u03b4 d supplied by manual correcting devices 72 74 of known type which enable small corrections to be made manually in the data p d therefore the corrected divergences p 39 d 39 of the cutting edge of the tool used with respect to a real or imaginary reference tool are available on the output lines 76 and 78 respectively of the adders 64 and 66 further serial digital adders 80 82 receive through the lines 54 76 and 58 78 respectively the two pairs of data x 2 p 39 and z 2 d 39 and supply as output on the lines 84 and 86 the artificial data x 39 2 z 39 2 respectively of diameter and longitudinal dimension of the part which takes account of the divergences of position of the tool used the instruction f for the rate of feed in mm revolution which is available on the line 52 is applied to a first input of a multiplying device 88 a second input of this multiplying device receives a signal n 39 through a line 90 from an adjustable frequency divider 91 driven through a line 93 by a signal n generated by a angular speed detector 92 associated with the mandrel of the lathe the signals n n 39 are.