On the QED Radiator at Order $\alpha^3$

The ${\cal O} (\alpha^3)$ leading logarithmic contribution to the QED radiator in the additive form is considered. The effect of the correction on two-fermion physics at LEP1 and LEP2 is evaluated and critically compared with the one of next-to-leading ${\cal O} (\alpha^2)$ corrections. A critical comparison with existing estimates for the LEP1 energy range is also performed. The ${\cal O} (\alpha^3)$ leading logarithmic corrections turn out to be relevant in view of the experimental precision already reached at LEP1 and foreseen at LEP2.