External field produced by a cylindrical electromagnet

IN some investigations by the authors during the Great War occasion arose to solve the following problems: Problem A. Given the dimensions and permeability of a straight cylindrical iron core, how many ampere-turns, uniformly distributed over the length of the core, are required to produce a given magnetizing force (magnetic field intensity) at a point on the axis of the core at a distance from its center large in comparison with its length?