Part 7/10:
The collaboration and exchange of ideas with Lord Kelvin, who presented his vortex atom theory, further inspired Maxwell. He began developing a comprehensive model utilizing vortex tubes to represent magnetic fields, with the motion of ball bearings symbolizing electric particles. This abstraction beautifully illustrated connections between these fields and led to the third equation.
Eventually, Maxwell found a more profound and less dependent framework, presenting his comprehensive theory in "A Dynamical Theory of the Electromagnetic Field" published in 1865. Here, he abstracted away the mechanical models in favor of a general, elegant formulation.