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The method which has been used hitherto for computing the alternating-current resistance and inductance of wires is to determine the differential equations of the magnetic field and solve these equations, taking into account the conditions imposed by the shape of the conductor. The author has developed a novel integration method. He divides the current into an infinite number of straight filaments. The magnetic field at any point is the sum of the magnetic fields of all the filaments, and the back e.m.f. in a filament is determined by the rate at which the magnetic fields of all the other filaments cut this filament. He first considers the case of the current in a cylindrical wire when the return current is so far away tha