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The usual transformations (UT) of the 3-vectors E and B that are found byLorentz, Poincar\'{e} and independently by Einstein in 1905. are generallyconsidered to be the Lorentz transformations (LT) of E and B. According to theUT E in one frame is 'seen' as E' and B' in a relatively moving frame. InMinkowski's last paper, in 1908. in section 11.6, he defined the vectors (withfour components) of the electric $\Phi $ and magnetic $\Psi $ fields anddiscovered that, e.g., $\Phi $ correctly transforms by the LT again to $\Phi^{\prime}$. His correct LT are reinvented in, e.g., [11] ([11] Ivezi\'{c} T2005 Found. Phys. Lett. 18 301). In this paper we show the essential similarityand some differences between Minkowski's relations in section 11.6 and theresults obtained in [11]. The low-velocity limit of the UT and the LT isbriefly examined. A short discussion of the comparison with the Trouton-Nobleexperiment is presented.

Lorentz Transformations of the Electric and Magnetic Fields According to Minkowski