Maxwell explicitly uses the imaginary part of a quaternion as a model of vectors, just as Hamilton did: > A german letter denotes a Hamilton vector, and indica

Maxwell explicitly uses the imaginary part of a quaternion as a model of vectors, just as Hamilton did: > A german letter denotes a Hamilton vector, and indicates not only its magnitude but its direction. The constituents of a vector are denoted with roman or Greek letters. [1] Gibbs and Heaviside or course use a different algebraic model of vectors, which is the one used in introductory courses now. But the more significant change made to get to "maxwells equations" as we know them now is not a slight change in the mathematical formalism. The big difference is a change in the underlying physical model: Maxwell's original treatment is largely in terms of potentials, which Heaviside modified to focus on the E-M force fields directly. This change is what gives the familiar four equations we know today, not fiddling with your parameterization of the rotation group, or similar games. Nowadays physicists frequently use a tensor or forms model of vectors in addition to the gibbs model. [1] https://archive.org/details/ATreatiseOnElectricityMagnetism-Volume2/page/n279 https://archive.org/details/ATreatiseOnElectricityMagnetism-...