The evolution of Maxwell´s equations through a brief critical examination of the history and background of the man and his times - Part 2

Maxwell\´s first published effort to describe electromagnetic phenomena was his paper "On Faraday\´s Lines of Force", published in 1855. In this first of four papers leading up to his Treatise, Maxwell opens his two-part presentation by stating in his introductory remarks that although much is known about the present state of electricity, areas still remain where knowledge is sparse and clear relationships have not been established. He goes on to say that it is necessary in any successful electrical theory to clearly show the connection between electricity at rest and current (moving) electricity, and the attractions and inductive effects of electricity in both states. Maxwell then asserts that in order to become familiar with the requirements of the science of electricity, one must become familiar with a large body of intricate mathematics, and that this in itself presents a significant hindrance to any progress. He goes on to express his desire to establish a method of investigation that would allow the grasp of a physical conception without creating a theory of the phenomena under study that relied on abstruse and purely analytical reasoning or that relied on a physical hypothesis before fully comprehending the various aspects of phenomena. Maxwell draws on his familiarity with Thomson\´s mathematical work to develop an analogical relationship between the flow of heat and the theory of action at a distance governed by an inverse square law.