James Clerk Maxwell advanced Electromagnetic theory, while also mathematically enlarging Michael Faraday’s works. He declined Newtonian mechanics for the formulation of new conceptual frameworks because more adequate for describing a field of new phenomena such as electromagnetism; so he also went beyond the Newtonian paradigm introducing a novelty in the relationship physics–mathematics based on new magnitudes, e.g., electric charge and energy instead of mass and force. However, through exactly which terms were these advances made? In particular, in A Treatise on Electricity and Magnetism, II, Part IV, Chapter IV–VII (1873) Maxwell aimed to formulate a dynamical justification for field equations; he focused on the fact that magnetic field appeared a complete kinetic energy system. In this paper, we analyse and describe both: (a) what he called, Lagrange’s method of reducing the ordinary dynamical equations in Mécanique analytique (1788)––including––three methods used by Maxwell for expressing the kinetic energy––detecting the existence of the terms of the form Tme, and (b) the application of the Lagrangian formulating through the equations of motion of a connected system.