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In this article values for the angles β and ν have been deduced (compare Fig. 3 and Eqs. (2) and (3)). New values have been deduced for the shear angle φ, Eqs. (16), (20), and (21). The increasing of the internal friction and the strain hardening have been considered. Equations for the work done in cutting per unit of length (6) and (13) have been deduced. For the cutting force Eqs. (14), (15), and (19) have been deduced. A high cutting speed decreases the friction angle τ between the chip and the face of the tool, by which the forces loading the machine tool steeply may be decreased. These forces are very highly dependent on the friction angle τ, since the rake angle α is negative. A new theory of the formation of a discontinuous chip is presented.