I was reading Einstein's seminal work: http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf Go to this part: II. ELECTRODYNAMICAL PART § 6. Transformation of the Maxwell-Hertz Equations for Empty Space. On the Nature of the Electromotive Forces Occurring in a Magnetic Field During Motion Einstein says "If we apply to these equations the transformation developed in § 3, by referring the electromagnetic processes to the system of co-ordinates there introduced, moving with the velocity v, we obtain the equations" But I'm not sure how applying the transformations obtains those equations. Can someone show me the intermediate steps?